What is the solution for 100000x^{''}+2100x^'+8x=2000 ?

The solution for 100000x^{''}+2100x^'+8x=2000 is x=c_{1}e^{-t/(200)}+c_{2}e^{-(2t)/(125)}+250

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100000x^{''}+2100x^'+8x=2000

100000 x^{^{''}} + 2100 x^{^{'}} + 8 x = 2000

x = c_{1} e^{- \frac{t}{200}} + c_{2} e^{- \frac{2 t}{125}} + 250

Solution steps

100000 x^{''} (t) + 2100 x^{'} (t) + 8 x = 2000

Solve linear ODE:

x = c_{1} e^{- \frac{t}{200}} + c_{2} e^{- \frac{2 t}{125}} + 250

x = c_{1} e^{- \frac{t}{200}} + c_{2} e^{- \frac{2 t}{125}} + 250

y^{^{''}} + y^{^{'}} - 27 = x e^{x}

y^{^{''}} + 5 y^{^{'}} - 9 y = e^{4 x}

D (x) = (x - \frac{11}{2})^{2} + x

y^{^{''}} - 7 y^{^{'}} - 18 y = - x + cos (3 x)

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

What is the solution for 100000x^{''}+2100x^'+8x=2000 ?
The solution for 100000x^{''}+2100x^'+8x=2000 is x=c_{1}e^{-t/(200)}+c_{2}e^{-(2t)/(125)}+250