What is the solution for y^{''}+5y^'=e^{-t},y(0)=-0,y^'(0)=1 ?

The solution for y^{''}+5y^'=e^{-t},y(0)=-0,y^'(0)=1 is y= 3/20+1/4-3/20 e^{-5t}-1/4 e^{-t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

Solution steps

y^{''} (t) + 5 y^{'} (t) = e^{- t}

Solve linear ODE:

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

y = \frac{3}{20} + \frac{1}{4} - \frac{3}{20} e^{- 5 t} - \frac{1}{4} e^{- t}

\int \frac{- y}{cot ( x )} d x

y^{^{''}} + 2 y^{^{'}} - 24 y = 0

x y + y^{^{'}} = 76 x

\int sin (9 x) d x

What is the solution for y^{''}+5y^'=e^{-t},y(0)=-0,y^'(0)=1 ?
The solution for y^{''}+5y^'=e^{-t},y(0)=-0,y^'(0)=1 is y= 3/20+1/4-3/20 e^{-5t}-1/4 e^{-t}