Differential equation Definition and 1000 Threads

Hey! :o I want to find the solution of the following initial value problem: $$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$ using Green's theorem but I got stuck... I found the following example in my notes...

I'm trying to build a circuit to solve the differential equation x''+2x'+x = f(t), where f(t) is a sine wave with frequency 5Hz and amplitude 0.5V. I am supposed to get a sine/cosine wave (as the diff. eq is just the same as the ove governing spring-mass forced oscillation) as solution, but...

Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...

I have a second order differential equation of the form (theta is a function of time): \theta ''=F\left(\theta ,\theta '\right) Turning them to two first order equations I get: \begin{cases} \theta '\:=\omega \\ \omega '=F\left(\theta ,\omega \right) \end{cases} And here's the algorithm...

Homework Statement Show that the radial eigenfunction unr,l is a solution of the differential equation: ħ2/2me×d2unr,l/dr2+[l(l+1)ħ2/2mer2 - e2/4πε0r]unr,l=Enr,lunr,lHomework Equations The radial function is R(r)=u(r)/r, so that the expression on the RHS is E×u. The Attempt at a Solution I know...

Homework Statement dy/dx=2xcos(y)-xy^3[/B]Homework EquationsThe Attempt at a Solution dy/dx=2xcos(y)-xy^3=x(2cosy-y^3) dy/(2cosy-y^3)=xdx [/B] I can not integrate the left side of the equation. Can someone help me please?

Homework Statement x(d^2y/dx^2)+dx/dt+xy=0 Homework EquationsThe Attempt at a Solution At first I thought it was an ODE, but then I found out the derivative was respect to to variables x and t. I am not sure if it is an ODE or PDE. What are the dependent and independent variables in the...

Homework Statement - The force acting on a particle m = 3kg is given by the following force equation: F = (v/9)(3 - x2), the particle begins at a position of x = 1m with a speed of v = 0 m/s at time t = 0s. Find the displacement of the particle at time t = 5 s. Homework Equations F =...

In my multivariable calculus class, we briefly went over Taylor polynomial approximations for functions of two variables. My professor said that the second degree terms include any of the following: $$x^2, y^2, xy$$ What surprised me was the fact that xy was listed as a nonlinear term. In...

I'm going through the solution to a problem that was assigned to my class and there's a step I don't really understand which I think is a concept I'm misunderstanding. 1. Homework Statement The curved surface of a cylinder of radius R and length L is insulated. The face at x = L is maintained...

Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2)[/B]Homework EquationsThe Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you need to take...

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...

Consider the second-order homogeneous linear differential equation $y'' + 4y' + Ky = 0$ Find the general solution if $K = 4$ So here is what I have: $r^2 + 4r + 4 = 0 $ =$(r + 2)(r+2)$ $r=-2$ ? But I thought that you can't do this because you won't be learning anything new if you have two of...

Hello! (Wave) I am looking at the following exercise: We consider the differential equation $x^2y'+2xy+1=0$, where $0<x< +\infty$. Show that each solutions goes to $0$ while $x \to +\infty$. Find the solution $\phi$ of the above differential equation so that $\phi(2)=2 \phi(1)$. That's...

Homework Statement Given that a particle has an initial velocity v0 and then undergoes an acceleration a = - bv. , where b is a constant, obtain an expression for v = v(t) and x = x (t) [/B]Homework Equations Not sure The Attempt at a Solution If I integrate a = - b v I think I get v +...

Find $y(x)$ to satisfy $$ y(x)=y'(x)+\int e^{2x}y(x) \, dx+\lim_{{x}\to{-\infty}}y(x)$$ given $$\lim_{{x}\to{0}}y(x)=0$$ and $$\lim_{{x}\to{\ln\left({\pi/2}\right)}}y(x)=1.$$

Homework Statement So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!) I am asked to solve this differential equation: y''+y'-2y=0 Homework Equations I know for a second order differential equation I can solve for the roots first. If...

dy/dx = (2y-x+5)/(2x-y-4) y(1)=1

Homework Statement This is actually a problem from my physics textbook, but I think it's mostly a mathematical problem, which is why I post it here: Show that the Langevin equation 1: \frac{dv}{dt}=-\gamma v+\frac{1}{m} F'(t) is solved by 2...

Okay, so I am a team member of a college robotics team, and this year we have quite challenging theme of playing badminton with robots, so for this reason we decided to track the position of shuttlecock in air. Now our approach was to predict the final position where it will land on ground from...

Homework Statement Kindly see the attachment. Homework Equations The Attempt at a Solution As with all such questions, its in setting everything up that I'm having some trouble. I know that F = mdv/dt + vdm/dt. And also that F = R - m(t)g, but R = M0g. From here though I don't know how to...

I have J - matrix x and y - vector d [ J(x) y(x)] / dx I can multiply the matrix and vector together and then differentiate but I think for my application it would be better to find an identity like {d [ J(x) y(x)] / dx } = J(x) d y(x) / dx + d J (x) / dx y(x) I am not sure if this identity...

I saw this in http://en.wikipedia.org/wiki/Momentum_operator From equation 4 to 5, it seems that a function is canceled out from the partial derivatives, is this possible?

Homework Statement Solve (xy+y2+x2) dx -( x2 )dy = 0 Homework Equations to verify if exact http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngM/[PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngy =...

How Can we define the degree of differential equation ? What is the degree of $$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)^{\!{2}}\left(\frac{dy}{dx}\right)^{\!{3}} +\left(\frac{dy}{dx}\right)^{\!{1}} =0$$ ??(Wondering)

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...

Find the general solution of the given differential equation.. $$(1+t^2)y' + 4ty = (1+t^2)^{-2}$$ I'm kind of confused here on what to do... Do I want to do something like $$e ^{\int4t} dt$$ and then multiply that through on both sides or do I need to do something different here..I'm not...

Hello, this is a maths problem that is related to a physics problem, but I think it's best posted here due to what I'm asking about. 1. Homework Statement \frac{d^{2}q}{dt^{2}} + \frac{R}{L} \frac{dq}{dt} + \frac{1}{LC}q = 0 is a differential equation describing how charge and current change...

Homework Statement use laplace transforms to solve the differential equation y"+2y'+17y = 1 Homework Equations Initial conditions are y(0) = 0 y'(0) = 0 The Attempt at a Solution so it converts to Y(s) (s^2+2s+17) = 1/s which then ends up as; Y(s) = 1/s*1/(s^2+2s+17) i know i need to invert...

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) +...

I know: f = ma f = - GMm/r^2 a = -GM/r^2 can be easily derived, But, we've been given the differential equation of motion of gas within a star as: a = -GM/r^2 - 1/p * dP(r)/dr I was wondering where the - 1/p * dP(r)/dr term is derived from? I can't find it in my textbooks. Cheers

I want to solve Equation (1). w is a constant: \begin{eqnarray} \text{Equation (1): }\frac{dx}{dt}=1+x^2w^2\end{eqnarray} and I have been told that it is solved by (2): \begin{eqnarray} \text{Equation (2): }x(t)=\frac{Ax(0)+B}{Cx(0)+D}\end{eqnarray} Problem I believe them, but before I keep...

Ok so I tried to solve the following differential equation for y by every method (variable separable method/making to variable separable method technique/putting y/x=other variable/making homogeneous to solve equation to get y/x ).But I think I can't solve this particular equation by these...

Homework Statement solve the following differential equation using Laplace transforms: y'' + 4y' + 4y = t^2 e^{-2t}, y_0 = 0, y'_0 = 0 y_0 and y'_0 are initial conditions. Homework Equations Using L to represent the Laplace transform, we have that L(y) = Y L(y') = pY - y_0 L(y'') =...

Hello all, I am currently trying to solve a differential equation numerically. The equation is as follows: dv/dt = (u*q)/(m0-q*t) - g - (cd*ρ*A*0.5)*v2 If you haven't already guessed, it's the rocket equation with added gravity and drag. Now, I'm not even sure if that's what it's supposed to...

Homework Statement Shown in attachment The problem has been modified. All inputs and outputs are 5 gal/min. Pure water enters tank 1. Homework Equations System of equations The Attempt at a Solution Included on attachment.

This is actually a chemistry problem, but I feel it's more appropriate posted here, as I'm not having trouble with the chemistry but rather the mathematics. To avoid mixing subjects, I'll keep chemistry jargon out. We're given the formula for a component, and the problem request we give...

Solve: $$\sin\left({x}\right)y''+(y'^2-\sin^2\left({x}\right))^{1/2}y'^2-\cos\left({x}\right)y'=0$$ Initial conditions: $y(0)=0$ $y'(0)=1$ Keep in mind that this question was on a Calc I exam worth 5 marks, so please nothing crazy like reduction of order or anything...:D

Salve, Can anybody recommend a book which has lots of differential practice problems?Or a similar book for Laplace transforms? No explanations just the answers and the problems,simply for practicing. Thanks for any help.

Homework Statement ##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)## What is ##m##? Homework EquationsThe Attempt at a Solution In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of...

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 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)...

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{\partial F(r,t)}{\partial t}=\alpha \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial F(r,t)}{\partial r} +g(r,t) $$ I have BC's: $$ \frac{\partial F}{\partial dr} = 0, r =0$$ $$ \frac{\partial...

Homework Statement I do not know how to find f(t) with the given Ampliture 40 and a=pi Homework EquationsThe Attempt at a Solution I have the solution above. my set up was 1/2y''+y'+5=f(t) 1/2S^2* Y(s) + Y(s)+5=f(t)

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...

Homework Statement When an object is submersed in a liquid, it experiences a buoyant force equal to the weight of the liquid displaced by the object. As an object moves through a liquid, there is a resistive force which is directly proportional to the density of the liquid, the cross sectional...

Any help is appreciated 1.)----Find the Character equation for the diff equation d^2y/dx^2-4dy/dx+3y=0 with initial conditions y(0)=0 and y'(0)=12 find the solution y(t) (this is what I have gotten so far on this part) p^2+4p+3=0 then (p-1)(p-3)=0 so p1=1 and p2=3? not really sure...

Homework Statement Find two power series solutions of the differential equation about the ordinary point x = 0. Homework Equations y'' + x^2y' +xy = 0 The Attempt at a Solution Check attachment. I found my y1 and y2, the boxed in answers are the ones the book says are the answers. Can...

Hi, I need suggestions for picking up some standard textbooks for the following set of topics as given below: Ordinary and singular points of linear differential equations Series solutions of linear homogenous differential equations about ordinary and regular singular points...

Homework Statement I used Lagrange to solve a problem and ended up with two differential equationsHomework Equations m_2x''+(k-m_2 {\theta '}^2)x=k(L_o+L_2/2)+m_2 g cos{\theta} and (I_1 +1_2 +m_2 x^2) {\theta}'' +2m_2 \cdot x \cdot x' \theta ' +(m_1 L_1/2 +m_2 x)g sin\theta =0The Attempt at...