Differential equations Definition and 999 Threads

For the first and second, I don't know if there is an analytical solution. The third I believe can only be solved with: $$ f(x,t)=c e^{\alpha \beta t}$$

So the other day, I was pouring beer from a can to a mug and I obviously know the flow rate depends on the height of the beer from the bottom of the can (fluid level in the vessel), angle of tilt and I think time as well. I was wondering how to best model the PDE to describe such a phenomenon (...

Hi all. I have another exam question that I am not so sure about. I've solved similar problems in textbooks but I have a feeling once again that the correct way to solve this problem is much simpler and eluding me. Especially because my answer to a) is already the solution to c) and d) (I did...

Hi all, I would like to know what is the equation upon which I can use to determine the practical resonance frequencies in a system of second order, linear differential equations. First some definitions: What I mean by practical resonance frequencies, is the frequencies that a second order...

Good evening, https://pdfs.semanticscholar.org/688b/e703a59a4a0c6fc96b4e42c38c321cd4d5b8.pdf Do you know :PROJECTIVE METHODS FOR STIFF DIFFERENTIAL EQUATIONS I have to make a program to solve a first-order differential equation according to this method but I do not arrive despite my efforts...

WHAT HAPPENS IS That I need to model the example of A Protein G example, using a function f in Matlab, but when I execute the script, the graphics I get do not correspond to those of the example. The problem is that I can not understand what the model seeks to represent, besides that I do not...

How can an ODE be symmetric? How would you plot an ODE to show off this property? (i.e. what would be the axes?)

When using the separation of variable for partial differential equations, we assume the solution takes the form u(x,t) = v(x)*g(t). What is the justification for this?

To write ##v## as a function of time, I wrote the equation ##m\frac{dv}{dt} = c_{2}v^2 + c_{1}v - mg \implies \frac{mdv}{c_{2}v^2 + c_{1}v - mg} = dt## To solve this, I thought about partial fractions, but several factors of ##-c_{1} \pm \sqrt {c_{1}^2 +4c_{2}*mg}## would appear and they don't...

I'm currently an undergrad student who had to take a break from school for over a year and its been around 3 or 4 years since I took Calc I - Calc III and Linear Algebra. I'm debating on taking a introduction to differential equations course as an elective that starts in a couple weeks when I...

Homework Statement Find an equation that defines IMPLICITLY the parameterized family of solutions y(x) of the differential equation: 5xy dy/dx = x2 + y2 Homework Equations y=ux dy/dx = u+xdu/dx C as a constant of integration The Attempt at a Solution I saw a similar D.E. solved using the y=ux...

Homework Statement On a certain island, there is a population of snakes, foxes, hawks and mice. Their populations at time t are given by s(t),  f (t), h(t), and m(t) respectively. The populations grow at rates given by the differential equations s'=(8/3)s - f - (1/3)h - (1/6)m f'=(2/3)s + f -...

Homework Statement (It should be noted that the actual problem has specific values associated with a, b, and c. However, at this point I'm trying to find a method to solve the problem rather than a specific solution). Homework Equations The Attempt at a Solution When I was trying to solve...

I'm facing a problem with that rhyming title up there. The design is thus: a downward-facing, vertical pipe with known constant flow and diameter has water flowing out of it, into a short (15cm-91cm) free fall. At the end of that fall is a bowl of indeterminate depth made of steel with holes...

Hi! I need your help for solving a couple of differential equation: dX/dt = a - b*X dY/dt = b*(c*exp(-E) - Y) - d*exp(-E)*Y X = X0 + f(Y, E) with X0, a, b, c and d are constants and f, a function of Z and E. Thank you in advance

I've a system of partial diff. eqs. in thermo-elasticity, I can solve it using normal mode analysis method but I need to solve it using laplace or Fourier

Afternoon, anyone that would like to take a look at this Differential Equation problem it would be very helpful. I have tried separating the problem, but I am only working with one known term. Consider the logistic equation $$\dot{y}=y(1-y). $$ (a) Find the solution satisfying $y_1(0)=6$ and...

Homework Statement I put this is the Calculus section because it relates to Calculus I and if I put it in Diff Eq section I think it would be assumed that I know the necessary terms, etc. My question is in regards to the use of the constant ##C## in differential equations. For reference, the...

Homework Statement Find Orthogonal Trajectories of ##\frac{x^2}{a}-\frac{y^2}{a-1}=1## Hint Substitute a new independent variable w ##x^2=w## and an new dependent variable z ##y^2=z## Homework EquationsThe Attempt at a Solution substituting ##x## and ##y## I get...

Homework Statement The question is to solve the inexact equation by turning it into exact.the equation is ##( x + y + 4 ) d x + ( - x + y + 6 ) d y = 0## Where "x" and "y" are variable. 2. Homework Equations [/B] 1.(x+y+4)=m and (-x+y+6)=n 2.Integrating Factor =##\frac { 1 } { x ^ { 2 } + y...

$$4\frac{\partial u}{\partial t}+\frac{\partial u}{\partial x} = 3u$$ , $$u(x,0)=4e^{-x}-e^{-5x}$$ let $$ U =X(x)T(t) $$ so $$4X\frac{\partial T}{\partial t}+T\frac{\partial X}{\partial x} = 3XT$$ $$4\frac{\partial T}{T \partial t}+\frac{\partial X}{X \partial x} = 3$$ $$\left(...

Homework Statement I have a coaxial cable with internal conductor of radius r1 and external conductor of radii r2 and r3. The material of the conductors has a conductivity ##\sigma_1##. Between the conductors there is a imperfect dielectric of conductivity ##\sigma_2##. Consider the...

Hi all! I need to give a presentation about a problem in class, but I can't seem to figure it out. This is the problem: Consider the system dr/dt = -j, dj/dt = r , where r (t) represents Romeo’s love (positive values) or hate (negative values) for Juliet at time t, and j(t) similarly...

<Moderator's note: Moved from a technical forum and thus no template.> Is what I have done correct ? I want to find v(t) from Sigma F = m*a. I have gravity force mg pointing downward with positive direction and resistive force R = -b*v^2 pointing upwards with negative direction are acting on a...

Classical physics is difficult because it is based on differential equations, and the differential equations of interest are usually unsolvable. The student must invest a lot of time in learning difficult math, and still can only analyze very simple systems. This difficulty arises in the first...

Homework Statement Hi there, I have an assignment which involves using reduction of order to solve for a second solution to an ode (the one attached). However this is a method I am new to, and though I have tried several times, I'm somehow getting something wrong because the LHS and RHS are not...

Hi, I'm attempting to learn differential equations on my own. Does anyone recommended a textbook that comes with/has a solution manual? I learn faster when I can see a problem worked out if I can't solve it. Thanks.

Homework Statement Solve the following differential equations/initial value problems: (cosx) y' + (sinx) y = sin2x Homework Equations I've been attempting to use the trig ID sin2x = 2sinxcosx. I am also trying to solve this problem by using p(x)/P(x) and Q(x) The Attempt at a Solution...

Homework Statement Solve the following differential equations/initial value problem: y^(4) - y'' - 2y' +2y = 0 Hint: e^-x sinx is a solution Homework Equations I was attempting to solve this problem by using a characteristic equation. The Attempt at a Solution y'''' -y'' -2y' + 2y = 0 -->...

Hello, could someone please give me some examples of where order linear non homogenous ordinary differential equations are used in physics[emoji4]

Hi, I was trying to solve the simplest problem of planetary motion (for one planet). The equations should be: ##F_x = m \frac {d^2x} {dt^2} = G \frac {Mmx} {r^3}## ##F_y = m \frac {d^2y} {dt^2} = G \frac {Mmy} {r^3}## where ## r = \sqrt{x^2 + y^2}## So I re-wrote the system like this...

Homework Statement z\frac{d^2z}{dw^2}+\left(\frac{dz}{dw}\right)^2+\frac{\left(2w^2-1\right)}{w^3}z\frac{dz}{dw}+\frac{z^2}{2w^4}=0 (a) Use z=\sqrt y to linearize the equation. (b) Use t=\frac{1}{w} to make singularities regular. (c) Solve the equation. (d) Is the last equation obtained a...

Can all differential equations be turned into algebraic equations by Fourier transform (FT)? If not, what kind of differential equations can be solved by the FT technique?

Homework Statement Homework EquationsThe Attempt at a Solution I managed to find dy/dx as follows: But I'm having difficulty finding the second derivative. I've looked at examples using the chain rule but I'm still confused. Would someone mind shedding some light on this for me?

Mixing with a Common Drain. Two tanks, each holding 1 L of liquid, are connected by a pipe through which liquid flows from tank A into tank B at a rate of 3-a L/min (0<a<3). The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 3 L/min. Solution flows out of...

Homework Statement I have derived the differential equations of a system. They are like the following: a\ddot{\theta} - b\ddot{x} + c \theta = 0 \\ d\ddot{\theta} + e\ddot{x} = F(t) where a,b,c,d,e are constants. I'm having trouble putting it into state space form, since I have the highest...

Hello, I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for...

i have used series solutions to differential equations many times but i never really stopped to think why it works i understand that the series solution approximates the solution at a local provided there is no singularity in which frobenius is used but i am not understanding how exactly it...

Homework Statement Homework Equations I have yet to figure out any relevant equations, but I do believe that the constraint equation for the optimization problem is the y=64-x^6 listed above. The Attempt at a Solution I am currently trying to figure out methods to begin my optimization...

Homework Statement I was never great in diffEQ, but now I have to solve this problem for physics homework and I'm pretty lost. d^4x/dx^4 - d^2x/dx^2 + a =0 Where a is a parameter.Homework EquationsThe Attempt at a Solution I have tried solutions like e^kt which work accept for the parameter...

Question - True or False: If $\frac{dx}{dt}$ = $\frac{1}{x}$ and $x$ = 3 when $t$ = 0, then $x$ is an increasing function of $t$. I understand how the graph of $x$ was obtained (the graph on the board), but I really don't understand why she attempted to draw the negative root of $x$ the way...

Hy folks, Upfront I want to apologize for my writing and my dissability to use correct symbols to ease readability of the example. Ok now that that's done I just want to start upfront. If we set a usual example of an object falling from a tower with a height of x meters and assume that the...

Homework Statement Hello. I'm trying to do some problem and I can't solve some differential equation from the 2nd degree: X'' - (F0 / ( d * m)) * X = 0 d, m, F are constant that are known Homework Equations I know that solution is a trigonometry equation. But I want to see how to solve...

Hey guys, when you're linearizing a function that has a constant, what do you do to it? An example would be y = x^2 + 3, would you just linearize it using its derivative and get rid of the constant?

Hi PF, initially I would like you to focus on that link https://books.google.com.tr/books?id=Dkp6CwAAQBAJ&pg=PA389&lpg=PA389&dq=runge+kutta+method++is+tvd+proof&source=bl&ots=47ULQDVwcC&sig=e2zjdnXENJ7WxBbrf6hXkSouvLI&hl=tr&sa=X&ved=0ahUKEwjU5Z2XsbXZAhUMCMAKHWpnATQ4ChDoAQhKMAQ#v=onepage&q=runge...

Homework Statement I am working through problem #1, a-c. Homework Equations The main equations are dx/dt=Ax, (A-rI)v=0, and det(A-rI)=0. The Attempt at a Solution [/B] Here is my attempt. I am fairly confident in my answer to A. I'm less sure on my answer to B, however it is the same as...

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

I'm so confused about this question :(

Hello! Currently I own Differential Equations by H.B Phillips, a really old book, but difficult and does it´s purpose. I have only 1 problem, certain exercises require certain geometrical functional study I suppose, for example: "find the equation of the curves so that the part of every tangent...