What is the solution for y^{''}+4000y^'+4000000y=36 ?

The solution for y^{''}+4000y^'+4000000y=36 is y=c_{1}e^{-2000t}+c_{2}te^{-2000t}+9/1000000

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y^{''}+4000y^'+4000000y=36

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 36

y = c_{1} e^{- 2000 t} + c_{2} t e^{- 2000 t} + \frac{9}{1000000}

Solution steps

y^{''} (t) + 4000 y^{'} (t) + 4000000 y = 36

Solve linear ODE:

y = c_{1} e^{- 2000 t} + c_{2} t e^{- 2000 t} + \frac{9}{1000000}

y = c_{1} e^{- 2000 t} + c_{2} t e^{- 2000 t} + \frac{9}{1000000}

What is the solution for y^{''}+4000y^'+4000000y=36 ?
The solution for y^{''}+4000y^'+4000000y=36 is y=c_{1}e^{-2000t}+c_{2}te^{-2000t}+9/1000000