How to solve initial value problems — Krista King Math | Online math help

SOLVED:What is an initial-value problem? Describe the sequence of steps for solving an initial-value problem.

SOLVED:Find the exact solution of the given initial value problem. Then apply Euler's method twice to approximate (to four decimal places) this solution on the given interval, first with step size h=0.01, then with step size h=0.005 . Make a table showing the approximate values and the actual value, together with the percentage error in the more accurate approximation, for x an integral multiple of 0.2. Throughout, primes denote derivatives with respect to x. y y^'=2 x^3, y(1)=3 ; 1 ≦x ≦2