Question

How do you do this question?

Answer 1

C. y₂ = (1 + (t/n))²

Explanation:

yₙ₊₁ = yₙ + Δt F(tₙ, yₙ)

yₙ₊₁ = yₙ + Δt yₙ

yₙ₊₁ = yₙ + (t/n) yₙ

When n=0:

y₁ = y₀ + (t/n) y₀

y₁ = 1 + (t/n)

When n=1:

y₂ = y₁ + (t/n) y₁

y₂ = 1 + (t/n) + (t/n) (1 + (t/n))

y₂ = 1 + (t/n) + (t/n) + (t/n)²

y₂ = 1 + 2(t/n) + (t/n)²

y₂ = (1 + (t/n))²