Question

Use the fourth-order Taylor series method to solve the initial value problem dy/dx = 3x + y^2,

y(0)=1 to approximate y(0.72), y(0.72+0.72), y(0.(3×72), y(0.(4×72)).

Answer 1

We have

f(t)=t+3 ∫0^t f(τ)dτ

 

When we apply Laplace function: