Differential equations Definition and 999 Threads

Homework Statement Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η, where θ=(T-T0)/(Ts-T0) EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

Homework Statement y3(dy/dx) = (y4 + 1)cosx 2. The attempt at a solution I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy. How should...

Ok so for this problem I have to use IVPs to prove that cos^2(x)+sin^2(x)=1. I know the end result is suppose to be: du/dt= - v, u(0)=1 dr/dt= u, v(0)=0 but I have no idea how to go about getting to this point.

I am working to use the artificial potential field method for path planning of mobile robot; actually I found in one of references the following description about this method: the artificial potential field method uses a scalar function called the potential function. This function has two...

Homework Statement The following series of differential equations represents a projectile's path when solved (g=9.81): Modify this series of differential equations to account for an additional force F with vector components a and b acting on the projectile. Here is a sample plot of this...

Homework Statement FIND i(t). [/B]Homework Equations VL = L*(di/dt) (Equation 1) IC = C*(dV/dt) (Equation 2) I(t) = e^-9*t*(A*cos(4.359*t) + B*sen(4.359*t)) A (Equation 3) The Attempt at a Solution I can get the exact value of the constant B as shown in the answer if I use -6 after the...

Homework Statement This is a problem regarding transient heat conduction in an undefined semi-infinite solid, initially at a temperature T0 whose surface temperature is suddenly raised to a new constant level at Ts. I also supplied the problem as an attachment for ease in explaining the...

I want to solve a Laplace PDE in a polar coordinate system with finite difference method. and the boundary conditions: Here that I found in the internet: and the analytical result is: The question is how its works? Can I give an example or itd?Thanks

Homework Statement Population Dynamics: Logistic model. Suppose the environmental carrying capacity of the population is 100000 and the growth rate a t=0 is 5%. . If the population starts at 10000, how long does it take for the population to reach half the carrying capacity? dp/dt = A P...

Hey, PF: If I have a function ##f(x)## where ##x## is itself a function of another variable (say time), is the following then true? $$f(x)=f(x(t))=f(t)$$ I ask this because if I have the following system of differential equations $$\frac{dA}{dt}=-Bb$$ $$\frac{dB}{dt}=-Aa$$ where litte ##a##...

A friend recently gave me a book on quantum mechanics. It's called Introduction to quantum mechanics. It's by David j griffiths. I am currently taking multivariable calc.I am taking linear algebra next semester. I want study this book, but I am wondering what mathi I need. My friend told me I...

When solving a separable differential equation, my textbook says this: ln|v-49|=-t/5+C→ |v-49|=e-t/5+C→ v=49+ce-t/5 What happened to the absolute values? I think it has something to do with the exponential always being positive.

I came across a few problems in the Kleppner and Kolenkow book in which you must find the force of tension at specific lengths on a rope of mass m. They said you must use differential equations to solve these types of problems. How can you solve and use differential equations like this to get...

Homework Statement Good day all! I'm stumped on a question: If I fire a bullet straight up what will be the initial velocity such that the bullet doesn't come back down? I need to model a differential equation (it will be first order) some how! Also, Gravity is not constant, but rather, the...

Hi everyone, First of all, this is an awesome place :) I'm looking for a differential equation book, with partial differential equation (and Fourier series solution) that really goes into physics. I'm a 3-year undergrad student in Physics so I already know a little about it. By the way, for now...

Good afternoon, I've been working my way through Serge Lang's series of textbooks, and I recently completed A First Course in Calculus. I'm currently working through the sequel to that book, Multivariable Calculus, and that should keep me tied up for at least two months. Looking ahead...

Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other...

Homework Statement On very hot days there sometimes can be a mirage seen hovering as you drive. Very close to the ground there is a temperature gradient which makes the refraction index rises with the height. Can we explain the mirage with it? Which unit do you need to extremalise? Writer the...

Homework Statement Good day all, My professor gave my class a packet of about 40 differential equations. I for the life of me cannot figure out how t solve these last 4! I also have an exam tomorrow morning, and would like finish these last few. I don't need them solved out, I would just...

Hello guys, I have the system of PDE below and I want to solve it using finite difference method but I think I have to reduce it first to a system of first order PDE. The problem is that I don't know how to reduce this PDE to a first order system. I will appreciate any hints in this regard...

I am working on a simple PDE problem on full Fourier series like this: Given this piecewise function, ##f(x) = \begin{cases} e^x, &-1 \leq x \leq 0 \\ mx + b, &0 \leq x \leq 1.\\ \end{cases}## Without computing any Fourier coefficients, find any values of ##m## and ##b##, if there is any...

Hi, I have previously made a post in order to gain some insight in my rather out of control project. Long story short I am investigating vibration of a circular plate and its standing waves. After consultation at this forum I have been guided in the direction of acoustics and bessel functions...

Homework Statement I am currently in quantum chemistry, and in class one day my professor spent some time talking about Maxwell's equations. I am looking at my notes, trying to piece together Maxwell's equations, differential equations, and the principle of superposition, since this is not in...

Homework Statement I need help finding the limit of the differential equation. (dx/dt) = k(a-x)(b-x) that satisfies x(0)=0 assuming a) 0<a<b and find the limit as t->infinity of X(t) b) 0<a=b and find the limit as t->infinity of X(t) Homework Equations none The Attempt at a Solution I...

I've been reviewing my knowledge on the technique of variation of parameters to solve differential equations and have a couple of queries that I'd like to clear up (particularly for 2nd order inhomogeneous ODEs), if possible. The first is that, given the complementary solution...

Hello. I can't seem to remember how to do these kind of problems. I need to determine the order of the differential equations. Can someone show how this is done so that I can understand how to do the rest? $\d{^2y}{x^2}+2\d{y}{x} \d{^3y}{x^3}+x=0$

I want to develop my feel for reading/interpreting differential equations, particularly in Physics applications (for developing models and understanding ones that others have developed). Are there any good books out there that present problems that require deriving governing differential...

Hi all, I need to understand these differential equations specially moving from the second order to the third order because i couldn't understand how they got to the result, what was exactly the principle: $$ y'=f(x,y) $$ $$ y''=\frac{df}{dx}(x,y(x)) = f_{x}(x,y) + f_{y}(x,y)y' = f_{x}(x,y) +...

Hey MHB. I'm going to be taking a course on differential equations. What can I expect? Is the course harder than Calc 3? Which of the Calc classes is it most similar to? Are there certain topics I should brush up on? I'm really scared about this class and I want to make sure I do well. Thanks :o...

How relevant is complex analysis to physics? I really want to take differential equations but I would have to change my schedule around way more than I want to. So, would anyone advise a physics major to to take complex analysis? Should I just change my schedule around so I can take differential...

Homework Statement I am given the following coupled differential equations: \begin{align} (r^2+1)\ddot{θ}+2r\dot{r}\dot{θ} &= u1\\ \ddot{r}-r\dot{θ}^2&=u2 \end{align} together with the following expression for the kinetic energy: \begin{align} T &= 0.5(r^2+1)\dot{θ}^2+0.5\dot{r}^2...

Homework Statement Consider the initial value problem for the system of first-order differential equations y_1' = -2y_2+1, y_1(0)=2 y_2' = -8y_1+2, y_2(0)=-1 If the matrix [ 0 -2 -8 0 ] has eigenvalues and eigenvectors L_1= -4 V_1= [ 1...

Homework Statement If the method of undetermined coefficients is used to find a particular solution yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should have the form: ?Homework EquationsThe Attempt at a Solution LHS r^3-r=0 roots= 0, 1 y_c(t)=c_1e^tRHS te^(-t)+2cos(t)...

Homework Statement y''-y=t-4e^(-t)Homework Equations method of undetermined coefficients The Attempt at a Solution solving for characteristic equation first y''-y=0 r^2-1=0 c_1e^(-t)+c_2e^(t) RHS particular solution t-4e^(-t) y_p(t)= At+B+Ce^(-t) y_pt'(t)=A-Ce^(-t) y_p''(t)=Ce^(-t)...

In my introductory ODE class we have focused mostly on linear differential equations. I know that nonlinear differential equations are much harder to solve, and I am wondering what exactly the "state of the art" methods are for dealing with them, or also what recent developments have been made...

Homework Statement We are just starting to learn about basic differential equations in Calc 2 and I learned about separable differential equations but I'm not familiar with this style, here's the question: Given the differential equation of the form ay"+by'+y=0, find constants a and b so that...

I have differential equations problem, the problem is: ##\frac{(y+1)^2}{y} dy = x^2 \ln x \ dx## Integrating both sides will yield: ##\frac{1}{2} y^2 + 2y + \ln y = \ln x \ . \frac{1}{3}x^3 - \frac{1}{9} x^3 + c## Is this the final solution? If not, what is the final solution?

Homework Statement Solve the given the two equations: xdy + ydx = ydy and (y^2 + 1)dx +(2xy + 1)dy = 0 Homework Equations N/A. The Attempt at a Solution For the first, I can see that solving this with respect to dy/dxmight be a bit tricky. However, if I solve it for dx/dy, things...

Homework Statement Solve the given initial value problem: y'' + y = u(t-\pi) - u(t-2 \pi) y(0) = 0 y'(0) = 1 Homework EquationsThe Attempt at a Solution First I took the Laplace transform of both sides: \mathcal{L}[y'' + y ] = \mathcal{L}(u(t-\pi)) - \mathcal{L}(u(t-2 \pi)) (s^{2}Y(s)...

Homework Statement Solve the given initial-value problem. y'' = 1 - u(t-1) y(0) = 0 y'(0) = 0 Homework EquationsThe Attempt at a Solution First I took the Laplace transform of both sides: \mathcal{L}(y'') = \mathcal{L}(1 - u(t-1)) s^{2}Y(s) - sy(0) - y'(0) = \mathcal{L}(1) -...

1. Homework Statement http://puu.sh/cSK1u/62e2f1c74d.png olve the system: x' = [-4, -4 4, -4] with x(0) = [ 2, 3] Find x1 and x2 and give your solution in real form.2. Homework Equations 3. The Attempt at a Solution Just a note here, I'm basically forced to self-learn this course because...

Hello! I'm trying to model a car slowing down from speed with the forces of drag and friction and gravity from the road slope.. The model, which models the resistive forces is as follows.. [ Ffriction + Fdrag + Fslope ] / m = -a (deceleration) where: Friction force Ffriction = A...

Hi guys, I´ve just started with SDE and Itô´s lemma but don't really know where and how to begin. I´ve realized that both a Reimann integral and Itô integral is needed both cannot figure out how to solve these questions. Would be much appreciated if someone would help me.

Working through Mathematical Methods in the Physical Sciences by Boas, on the chapter on Series Solutions of Differential Equations, Boas works the example: y' = 2xy Boas differentiates the series representation of y yielding y', substitutes both into the original equation, and expands...

Homework Statement Y' = [ -14 0 12 24 -2 24 16 0 14 ] Y Subject to the condition y_1 (0) = -6, y_2 (0) = 11, y_3 (0) = 8, find: y_1(t), y_2(t), y_3(t) Homework EquationsThe Attempt at a Solution This is more just to see if my answers are correct than anything, so I begin...

Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4Homework EquationsThe Attempt at a Solution Im really not sure how to go...

Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...

Homework Statement A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the...

Good evening everyone, I hope everyone is having a better evening than myself thanks to this homework problem. Let P be the set of positive numbers. For a,b in P, define a+b=a x b; for a in P and a real number r, define r x a= a^r. Show that P is a vector space using ⊕ as addition and (circle...