- #1
camilus
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- Find the eigenvalues and eigenfunctions for the given boundary-value problem.
[tex]{d \over dx}[x{dy \over dx}] + {\lambda \over x}{y} = 0, [/tex] subject to [tex] y(1)=0, y'(e^\pi)=0[/tex]
- Find the eigenvalues and eigenfunctions for the given boundary-value problem.
[tex]{d \over dx}[{1 \over 3x^2+1}{dy \over dx}] + {\lambda (3x^2+1)}{y} = 0, [/tex] subject to [tex] y(0)=0, y(\pi)=0[/tex]
hint: let [tex]t=x^3+x[/tex]
- Find the general solution of the Cauchy-Euler equation Assume x>0.
[tex]x^3{d^3y \over dx^3} - 4x^2{d^2y \over dx^2} + 8x{dy \over dx} - 8y = 4ln(x)[/tex]
- Use teh variation of parameters to find the general solution of the given differential equation.
[tex]{d^2y \over dx^2} +y = {1 \over 1+sin x}[/tex]
- Given that [tex]y_1(x)=x[/tex] is a solution of the DE [tex](1-x^2)y'' - 2xy' + 2y = 0, -1<x<1,[/tex] use the reduction of order to find a second solution (Do not use the formula.)
- Use the method of undetermined coefficients to find the general solution of the give DE.
[tex]y''+y = x sinx[/tex]
I need a lot of help here! In a little bit, I'll post my work so far, which should lead you in the right direction.