What is the solution for y^{''}+6y^'+5y=36e^x ?

The solution for y^{''}+6y^'+5y=36e^x is y=c_{1}e^{-x}+c_{2}e^{-5x}+3e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+6y^'+5y=36e^x

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + 3 e^{x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 36 e^{x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + 3 e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + 3 e^{x}

y^{^{'''}} - y^{^{''}} = x - 2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = cos^{2} (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3 x}}{x ^{2} + 1}

y^{^{''}} - 2 y + 5 y = 1, + e^{- t} y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + y = x cos (2 x)

What is the solution for y^{''}+6y^'+5y=36e^x ?
The solution for y^{''}+6y^'+5y=36e^x is y=c_{1}e^{-x}+c_{2}e^{-5x}+3e^x