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

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7
votes
2answers
89 views
+50

Explicit traveling wave solution for the diffusion equation

Find explicit formulas for $v$ and $\sigma$ so that $u(x,t)=v(x-\sigma t)$ is a traveling wave solution of the nonlinear diffusion equation $$u_t-u_{xx}=f(u)$$ where $$f(z)=-2z^3+3z^2-z$$ and ...
3
votes
1answer
46 views
+50

Writing solution to an arbitrary ODE with arbitrary initial values as the sum of a power series?

Let $f(t), g(t)$ be polynomials, and let $y$ be a function of $t$. Given the ODE $y'' + f(t) y' + g(t) y = 0$ with initial conditions $y(0) = \alpha$ and $y'(0) = \beta$, write $y$ as the sum of a ...
2
votes
0answers
28 views
+100

Find the indicial equation

How do i find the indicial equation to $x^2y''+4xy'+4y=12-12x^2$ I used the frobenius method but got stuck: $x^2y''+4xy'+4y-12+12x^2=0$ $x^2(y''+12)+4xy'+4y-12=0$ ...