What is the solution for (d+2)(d-1)^2y=e^{-2}x+2sinh(x) ?

The solution for (d+2)(d-1)^2y=e^{-2}x+2sinh(x) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d+2)(d-1)^2y=e^{-2}x+2sinh(x)

(d + 2) (d - 1)^{2} y = e^{- 2} x + 2 sinh (x)

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + e^{- 2 x} \cdot \int \frac{e ^{2 x - 2} ( x + 2 e ^{2} sinh ( x ) )}{9} d x + e^{x} \cdot \int - \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) ) ( 3 x + 1 )}{9} d x + e^{x} x \cdot \int \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) )}{3} d x

Solution steps

(d + 2) (d - 1)^{2} y = e^{- 2} x + 2 sinh (x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + e^{- 2 x} \cdot \int \frac{e ^{2 x - 2} ( x + 2 e ^{2} sinh ( x ) )}{9} d x + e^{x} \cdot \int - \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) ) ( 3 x + 1 )}{9} d x + e^{x} x \cdot \int \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) )}{3} d x

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + e^{- 2 x} \cdot \int \frac{e ^{2 x - 2} ( x + 2 e ^{2} sinh ( x ) )}{9} d x + e^{x} \cdot \int - \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) ) ( 3 x + 1 )}{9} d x + e^{x} x \cdot \int \frac{e ^{- x - 2} ( x + 2 e ^{2} sinh ( x ) )}{3} d x

What is the solution for (d+2)(d-1)^2y=e^{-2}x+2sinh(x) ?
The solution for (d+2)(d-1)^2y=e^{-2}x+2sinh(x) is