# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### Integrating factors, a missing solution

I want to solve the differential equation $(3xy+y^2)+(x^2+xy)y'=0$. If I use the integrating factor $\mu (x)=x$ so that the original differential equation becomes exact, then the general solution that ...
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For $\alpha, \beta>0$ the differential equation, I am trying to solve, is given by $$\begin{pmatrix}\dot x_1\\\dot x_2\end{pmatrix}=\alpha\sin(x_1^2+x_2^2)\begin{pmatrix}x_2\\-x_1\end{pmatrix}+\... 3answers 68 views ### 3rd order differential equation with variable coefficients How to do I solve this differential equation?$$ x^3 u′′′ + x^2 u′′ + x u′= 0. $$The series solution method is not working in this case. 1answer 25 views ### How to solve a nonlinear second order differential equation? I have been trying to find ways to solve:$$J\frac{d²\theta(t)}{dt²}-K_m cos(\theta(t))=-\tau_f$$With the initial conditions$$\theta(t=0)=0\frac{d\theta}{dt}(t=0)=0$$Without success. Is that ... 4answers 77 views ### Find an equation of the curve that passes through the point (0, 6) and whose slope at (x, y) is \frac{x}{y}. Book wasn't helpful. I am using James Stewarts Early Transcendentals Calculus, and Section 9.3 (which is where this problem comes from) doesn't seem to have anything remotely similar to the problem I am facing. No ... 1answer 78 views ### Proving J_n(x)N_{n+1}(x)-J_{n+1}(x)N_n(x)=-\dfrac{2}{\pi x}: Part 1 of 3 This is the first part of a proof that J_n(x)N_{n+1}(x)-J_{n+1}(x)N_n(x)=-\dfrac{2}{\pi x}: Write Bessel's equation$$x^2y^{\prime\prime}+xy^{\prime} + (x^2 - p^2)y=0\tag{1}$$with y=J_p and ... 1answer 29 views ### Solving \sin(\sqrt{\lambda}L) + \beta \cos(\sqrt{\lambda}L)\sqrt{\lambda} = 0 I'm working with the ODE$$-\frac{d^2u}{dx^2}=\lambda u$$and trying to find eigenvalues and eigenfunctions corresponding the boundary conditions$$u(0)=0, u(L)+\beta \frac{du}{dx}(L)=0 Assuming ...
I have a problem solving this differential equation using Laplace transformation. $y'' -9y=0 , \ y(0)=1 , \ y'(0)=0$