Series solution Definition and 102 Threads

Problem y^{\prime} = x^2 y General Comments There must be some kind of flaw in my solution as I don't get to the same result as the one my book provides: y = c_0 \sum _{n=0} ^{\infty} \frac{x^{3n}}{3^n n!} = c_0 e^{x^3 / 3} \qquad \fbox{CORRECT ANSWER} Any help is highly...

I am trying to find the power series solution of y' = x^2y but don't know how to arrive at the answer of y = a_0exp(x^3/3). [I know that it's an easily solved separable equation, I'm just trying to figure out how to find the power series solution] My solution so far: Assume y...