solve the initial value problem.

Question

f ' (x)=sqrt(x)+x^2 when f(0)=2

please do it step by step because I don't understand this topic

Answer 1

y' = x^(1/2) + x^2

integrating:

y = (2/3)x^(3/2) + (1/3)x^3 + c

f(0)=2 ---> 2 = c

y = (2/3)x^(3/2) + (1/3)x^3 + 2