What is the solution for y^{''}+12y^'+37=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+12y^'+37=0,y(0)=1,y^'(0)=0 is y=1+37/144-37/144 e^{-12t}-(37t)/(12)

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y^{''}+12y^'+37=0,y(0)=1,y^'(0)=0

y^{^{''}} + 12 y^{^{'}} + 37 = 0, y (0) = 1, y^{^{'}} (0) = 0

y = 1 + \frac{37}{144} - \frac{37}{144} e^{- 12 t} - \frac{37 t}{12}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 37 = 0

Solve linear ODE:

y = 1 + \frac{37}{144} - \frac{37}{144} e^{- 12 t} - \frac{37 t}{12}

y = 1 + \frac{37}{144} - \frac{37}{144} e^{- 12 t} - \frac{37 t}{12}

y^{^{''}} - y^{^{'}} = 2 t^{2} + t - 1

y^{^{''}} - 2 y = 12 x - 10

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

y^{^{'''}} + y^{^{''}} = x + 1

y^{^{''}} + y - 20 y = (x + 1) e^{x}

What is the solution for y^{''}+12y^'+37=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+12y^'+37=0,y(0)=1,y^'(0)=0 is y=1+37/144-37/144 e^{-12t}-(37t)/(12)