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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'}} = 8 x + y, y (0) = 6

\frac{\partial}{\partial z} (e^{x} + yz)

f (x)

x \to 6 + lim (\frac{x}{36 - x ^{2}})

\frac{d}{d x} (2 x arcsin (x))

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