Решить задачу Коши. 1. y'=3e^x+1 y(0)=1 2.y"=(x/6)+sin(x) y(0)=3 y"(0)=1

Question

Решить задачу Коши.
1. y'=3e^x+1 y(0)=1

2.y"=(x/6)+sin(x) y(0)=3 y"(0)=1

Answer 1

1. y = 3eˣ + x + C

y(0) = 3 + C = 1 => C = -2

y = 3eˣ + x - 2

2. y' = x²/12 - cosx + C₁

y'(0) = -1 + C₁ = 1 => C₁ = 2

y = x³/36 - sinx + 2x + C₂

y(0) = C₂ = 3

y = x³/36 - sinx + 2x + 3