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...