An explicit forward Euler method is used to numerically

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An explicit forward Euler method is used to numerically integrate the differential equation
dy = y
dt

using a time step of 0.1. With the initial condition y(0) = 1, the value of y(10) computed by this method is ______ (correct to two decimal places).

1. 21.5937
2. 25.937
3. 2.5937
4. 1 21.15937

Correct Option: C

General formula
y_{n + 1} = y_n + h_f(t_n , y_n)
For n = 0, y₁ = y₀ + h_f (t₀, y₀)
= y₀ + hy₀
= 1 + 0.1 (1)
y₁ = 1.1
For n = 1, y₂ = y₁ + h_f (t₁, y₁)
= y₁ + hy₁
= 1.1 + 0.1 (1.1)
y₂ = 1.21
For n = 2, y₃ = y₂ + h_f (t₂, y₂)
= y₂ + hy₂
= 1.21 + 0.1 × 1.21
y₃ = 1.331
For n = 3, y₄ = y₃ + h_f (t₃, y₃)
= y₃ + hy₃
= 1.331 + 0.1 × 1.331
y₄ = 1.4641
For n = 4, y₅ = y₄ + h_f (t₄, y₄)
= y₄ + hy₄
= 1.4641 + 0.1 × (1.4641)
y₅ = 1.61051
For n = 5, y₆ = y₅ + h_f (t₅, y₅)
= y₅ + hy₅
= 1.61051 + 0.1 × 1.61051
y₆ = 1.771561
For n = 6, y₇ = y₆ + h_f (t₆, y₆)
= y₆ + hy₆
= 1.771561 + 0.1 × 1.771561 = 1.9487
For n = 7, y₈ = y₇ + h_f (t₇, y₇)
= y₇ + hy₇
= 1.9487 + 0.1 × (1.9487)
y₈ = 2.14357
For n = 8, y₉ = y₈ + h_f (t₈, y₈)
= y₈ + hy₈
= 2.14357 + 0.1 × 2.14357
y₉ = 2.3579
For n = 9, y₁₀ = y₉ + h_f (t₉, y₉)
= y₉ + hy₉
= 2.3579 + 0.1 × (2.3579)
y₁₀ = 2.5937