What is the solution for y^{''}+7y^'+12y=21e^{3t} ?

The solution for y^{''}+7y^'+12y=21e^{3t} is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/2 e^{3t}

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y^{''}+7y^'+12y=21e^{3t}

y^{^{''}} + 7 y^{^{'}} + 12 y = 21 e^{3 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{2} e^{3 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 12 y = 21 e^{3 t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{2} e^{3 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{1}{2} e^{3 t}

y^{^{''}} + 3^{2} y = 6 \cdot sin (3 x)

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 3 x

y^{^{''}} + 2 y^{^{'}} + y = cos (3 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = e x cos (2 x)

What is the solution for y^{''}+7y^'+12y=21e^{3t} ?
The solution for y^{''}+7y^'+12y=21e^{3t} is y=c_{1}e^{-3t}+c_{2}e^{-4t}+1/2 e^{3t}