please help, i need to review for final but dont know how to do this poblem.......?

Question

Find 3rd degree taylor polynomial at (use x.. to distinguish from other x) x..=0 for the solution of the initial value problem dy/dx= x^3+3y^2 , y=2 at x=0. thanks

Answer 1

Try differentiating two more times and evaluating everything at x=0 to get the second and third derivatives of y, which you can then use to get the Taylor exansion of y to the third order.