# ordinary differential equation

1. ### A Determine PDE Boundary Condition via Analytical solution

I am trying to determine an outer boundary condition for the following PDE at $r=r_m$: $$\frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t}$$...
2. ### I Y'' + y = 0 solution and recursion relation

I've found the general solution to be y(x) = C1cos(x) + C2sin(x). I've also found a recursion relation for the equation to be: An+2 = -An / (n+2)(n+1) I now need to show that this recursion relation is equivalent to the general solution. How do I go about doing this? Any help would be...
3. ### I About Arnold's ODE Book Notation

In Arnold's book, ordinary differential equations 3rd. WHY Arnold say Tg:M→M instead of Tg:G→S(M) for transformations Tfg=Tf Tg, Tg^-1=(Tg)^-1. Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a...
4. ### Vladimir I. Arnold ODE'S book, about action group

hi everyone, i'm electrical engineer student and i like a lot arnold's book of ordinary differential equations (3rd), but i have a gap about how defines action group for a group and from an element of the group.For example Artin's algebra book get another definition also Vinberg's algebra book...
5. ### Solving Partial Differential Equation

1. The problem statement, all variables, and given/known data Task requires you to solve a partial differential equation $$u_{xy}=2yu_x$$ for $u(x,y)$. A hint is given that a partial differential equation can be solved in terms of ordinary differential equations. According to the solution...
6. ### I How to find a solution to this linear ODE?

I want to find solution to following ODE $$\frac{d \bar h}{dt} + \frac{K}{S_s} \alpha^2 \bar h = -\frac{K}{S_s} \alpha H h_b(t)$$ I have solved it with integrating factor method with $I=\exp^{\int \frac{1}{D} \alpha^2 dt}$ as integrating factor and $\frac{K}{S_s} = \frac{1}{D}$ I have...
7. ### A How to simplify the solution of the following linear homogeneous ODE?

During solution of a PDE I came across following ODE $\frac{d \bar h}{dt} + \frac{K}{S_s} \alpha^2 \bar h = -\frac{K}{S_s} \alpha H h_b(t)$ I have to solve this ODE which I have done using integrating factor using following steps taking integrating factor I=\exp^{\int \frac{1}{D} \alpha^2...
8. ### Wondering if these two First Linear Order IVPs are correct

1. Homework Statement I am having trouble proving if the equation i have found for number 1 is correct. I have posted my solution to get back to the main problem in the first photo below. For number 2 I am having trouble isolating for 1 y(x). Did i do the integration and setup properly? 2...
9. ### Basis for the space of solutions (ODE)

1. Homework Statement The equation given: dy/dt = 3*y A basis for the space of solutions is required. 3. The Attempt at a Solution According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t)...
10. ### Introducing SHM to high school students

I need to introduce Simple Harmonic Motion to a group of high school students studying physics. They don't know anything about differential equation except the method of separation of variables. Also, they have limited knowledge on complex numbers like eiωt. However, I don't want to just give...
11. ### Is there a mistake in the assignment?

1. Homework Statement I'm actually a tutor, and a student of mine at uni has the following differential equation with initial conditions to solve imgur link: http://i.imgur.com/ptuymQv.gif From y(t) = c_1sin(3t) + c_2cos(3t), it is not possible to solve for the constants using the given...
12. ### A non-exact nonlinear first ODE to solve

1. Homework Statement Solve the following equation. 2. Homework Equations ( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0 3. The Attempt at a Solution M = ( 3xy4 + 2xy ) N = ( 2x3y3 - x2 ) ∂M/∂y = 12x2y3 + 2x ∂N/∂x = 6x2y3 - 2x Then this equation looks like that the integrating factor is...
13. ### The Dirac Delta Function

1. Homework Statement Differential equation: $Ay''+By'+Cy=f(t)$ with $y_{0}=y'_{0}=0$ Write the solution as a convolution ($a \neq b$). Let $f(t)= n$ for $t_{0} < t < t_{0}+\frac{1}{n}$. Find y and then let $n \rightarrow \infty$. Then solve the differential equation with...
14. ### I General solution to linear homogeneous 2nd order ODEs

Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where $c_{1},c_{2}$ are arbitrary constants and $y_{1}(x), y_{2}(x)$ are linearly independent basis solutions. How does one prove that...
15. ### Find a function with given condition

1. Homework Statement Find a curve that passes through point A(2,0) such that the triangle which is defined with a tangent at arbitrary point M, axis Oy and secant \overline{OM} is isosceles. \overline{OM} is the base side of a triangle. 2. The attempt at a solution Function passes through...
16. ### Application of boundary conditions in determining the Green's function

1. Homework Statement Find the Green's function $G(t,\tau)$ that satisfies $$\frac{\text{d}^2G(t,\tau)}{\text{d}t^2}+\alpha\frac{\text{d}G(t,\tau)}{\text{d}t}=\delta(t-\tau)$$ under the boundary conditions $$G(0,\tau)=0~~~\text{ and }~~~\frac{\text{d}G(t,\tau)}{\text{d}t}=0\big|_{t=0}$$ Then...
17. ### Applied Any books on Ordinary Differential Equations w/ applications

Hello, I really need a good book on ordinary differential equations with applications on Quantum Mechanics, as I will be attending a course on QM but I do not have the proper mathematical background that is needed.
18. ### Solve a 2nd order Ordinary Differential Equation

1. Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e 2. Homework Equations No clue how to start this 3. The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0
19. ### Laplace transform of y''(t')

The ordinary differential equation, with initial values,shall be solved using Laplace transform. The ODE looks like this $$y''(t')+2y''(t)-2y(t)=0$$ And the initial conditions are $$y(0)=y'(0)=0, y''(0)=0$$ The problem is with the first...
20. ### Matrix-free iteration methods and implicit ODE solvers

Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...
21. ### Confusing particular integral

Homework Statement Well I am looking for the particular integral of: d2y/dt2 + 4y = 5sin2t The attempt at a solution As f(t) = 5sin2t, the particular integral yPI should look like: yPI = Acos2t + Bsin2t dyPI/dt = -2Asin2t + 2Bcos2t d2yPI/dt2 = -4Acos2t - 4Bsin2t Subbing in to the differential...
22. ### A discussion about Fourier and Laplace transforms and calculus

i have read many of the answers and explanations about the similarities and differences between laplace and fourier transform. Laplace can be used to analyze unstable systems. Fourier is a subset of laplace. Some signals have fourier but laplace is not defined , for instance cosine or sine...
23. ### Kinematics / ODEs problem

1. Homework Statement I stumbled upon a problem and i can't establish the ODE to solve it, from there on i believe i can solve the ODEs if they have regular analytical solving methods (translated from Spanish, will sound a bit weird) Car race, 2 pilots (a and b) participate in a drag race. They...