Question

How do you do this question?

Answer 1

y₂ = 0.33253

Explanation:

yₙ₊₁ = yₙ + Δt F(tₙ, yₙ)

yₙ₊₁ = yₙ + Δt (yₙ − 1) (1 − tₙ²)

yₙ₊₁ = yₙ + Δt (yₙ − 1) (1 − (nΔt)²)

When n = 0:

y₁ = y₀ + Δt (y₀ − 1) (1 − t₀²)

y₁ = 0.7 + 0.9 (0.7 − 1) (1 − 0²)

y₁ = 0.43

When n = 1:

y₂ = y₁ + Δt (y₁ − 1) (1 − t₁²)

y₂ = 0.43 + 0.9 (0.43 − 1) (1 − 0.9²)

y₂ = 0.33253