Solve Series Equation: xy+(sinx)y'+2xy=3x^2, y(0)=y'(0)=1

[angelas]

Hi everyone,
Can anyone help me find the solution of this equation using series?

xy"+(sinx)y'+2xy=3x^2
y(0)=y'(0)=1

Thanks in advance

 

[Galileo]

Sure, what have you got so far?

 

[angelas]

Sure, what have you got so far?

I know that 0 is an ordinary point and therefore I can write the solution in form of series. But I don't know what to do with sin x.

 

[Galileo]

If you assume a series solution you have to compare coefficients later on, so it would help if sin x is written as a series.