What is the solution for y^{''}-4y^'-21y=800e^{-t} ?

The solution for y^{''}-4y^'-21y=800e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-3t}-50e^{-t}

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y^{''}-4y^'-21y=800e^{-t}

y^{^{''}} - 4 y^{^{'}} - 21 y = 800 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 50 e^{- t}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 21 y = 800 e^{- t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 50 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 3 t} - 50 e^{- t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 13 t e^{4 t}

y^{^{''}} - 2 y^{^{'}} - 8 y = (x + 1) e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 56 cos (3 x)

(d^{2} + 6 d + 10) y = 3 e^{- 3 x} x - 2 e^{3 x} cos (x)

D u = 50 - \frac{30}{100} \frac{1}{500}

What is the solution for y^{''}-4y^'-21y=800e^{-t} ?
The solution for y^{''}-4y^'-21y=800e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-3t}-50e^{-t}