What is the solution for y^{''}+200y^'+1000000=0 ?

The solution for y^{''}+200y^'+1000000=0 is y=c_{1}+c_{2}e^{-200t}-5000t

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y^{''}+200y^'+1000000=0

y^{^{''}} + 200 y^{^{'}} + 1000000 = 0

y = c_{1} + c_{2} e^{- 200 t} - 5000 t

Solution steps

y^{''} (t) + 200 y^{'} (t) + 1000000 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 200 t} - 5000 t

y = c_{1} + c_{2} e^{- 200 t} - 5000 t

f^{^{''}} (t) + f (t) = cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 4 t}, y (0) = 1

y^{^{''}} - y^{^{'}} = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 16 = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} = 6 x + 6 - 2 e^{4 x}

What is the solution for y^{''}+200y^'+1000000=0 ?
The solution for y^{''}+200y^'+1000000=0 is y=c_{1}+c_{2}e^{-200t}-5000t