Solving Ordinary Differential Equations Using Picard's Method

Question

Given that f'(t) =dy/dt = t*ey ; y(0) = 0.

Determine the value of y using Picard's method when t = 0:3. (Use 2 iterations)

Answer 1

x₀ = 0, y₀ = 0, f'(t) = te^y

y = ∫₀^t te^ydt

When t = 0.3

y₁ = ∫₀^t t dt = t²/2 = 0.045

y₂ = ∫₀^tte^y1dt = t²e^y1/2 = (.3)²e^0.045 = 0.047