What is the solution for y^{''}+100y^'+1/(0.0004)y=30,y(0)=0 ?

The solution for y^{''}+100y^'+1/(0.0004)y=30,y(0)=0 is y=-0.012e^{-50t}+c_{2}e^{-50t}t+0.012

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y^{''}+100y^'+1/(0.0004)y=30,y(0)=0

y^{^{''}} + 100 y^{^{'}} + \frac{1}{0.0004} y = 30, y (0) = 0

y = - 0.012 e^{- 50 t} + c_{2} e^{- 50 t} t + 0.012

Solution steps

y^{''} (t) + 100 y^{'} (t) + \frac{1}{0.0004} y = 30

Solve linear ODE:

y = - 0.012 e^{- 50 t} + c_{2} e^{- 50 t} t + 0.012

y = - 0.012 e^{- 50 t} + c_{2} e^{- 50 t} t + 0.012

What is the solution for y^{''}+100y^'+1/(0.0004)y=30,y(0)=0 ?
The solution for y^{''}+100y^'+1/(0.0004)y=30,y(0)=0 is y=-0.012e^{-50t}+c_{2}e^{-50t}t+0.012