Second order differential equation

[sara_87]

Homework Statement

find the general solution to the second order ode:
x⁴y''+2x³y'+y=0

Homework Equations

using Euler's method

The Attempt at a Solution

assume that the solution is y=x^a
then y'=ax^a-1 and y''-a(a-1)x^a-2
substituting these into the ode:
a(a-1)x^a+2ax^a+x^ax^-2=0
which gives
a²+a+x^-2=0

and this is where i got stuck.
thank you

 

[HallsofIvy]

?? You say "use Euler's method". That is a numerical method of solving differential equations. What you are doing has nothing to do with Euler's method.

 

[sara_87]

I think i made a mistake. I thought when we use the assumption y=x^a that this is called Euler's method. but now i know it has nothing to do with it :)