Answer:
y₂ = 0.33253
Step-by-step 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
