What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x is y=c_{1}e^x+c_{2}e^{-5x}+4xe^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + 4 x e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 5 x} + 4 x e^{x}

y = c_{1} e^{x} + c_{2} e^{- 5 x} + 4 x e^{x}

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x is y=c_{1}e^x+c_{2}e^{-5x}+4xe^x