Find y as a function of x if x2y′′+13xy′+36y=x2, y(1)=5, y′(1)=−2.

Answer 1

This is a long one. I'll start you off in one way. You could use a power series solution, but you might recognize that this as an Euler-Cauchy problem (here is the link to an explanation): Euler Differential Equation -- from Wolfram MathWorld . There is a closed-form solution that you can get from the calculator on Wolframalpha.

Good luck!