Mathematics Homework Help

Obtain terms to order k of the particular solution of the following differential equation, where k is the number shown alongside each equation. use two methods. Also find an interval of convergence of series solution. 

the series methods are: successive differentiations, and undetermined coefficients. 

y’ = x^2-y^2; 

y(0) = 1 

k = 4 

the solution has to be: 

y = 1 – x + x^2 -(2/3)x^3+(5/6)x^4- ….., |x| < 0.069 

it is an easy problem. but I just want to check if my steps are fine or not.