What is the solution for y^{''}+y^'-12y=2e^{5t} ?

The solution for y^{''}+y^'-12y=2e^{5t} is y=c_{1}e^{3t}+c_{2}e^{-4t}+1/9 e^{5t}

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y^{''}+y^'-12y=2e^{5t}

y^{^{''}} + y^{^{'}} - 12 y = 2 e^{5 t}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{9} e^{5 t}

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = 2 e^{5 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{9} e^{5 t}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{1}{9} e^{5 t}

\frac{1}{2} x^{^{''}} + 2 x^{^{'}} + 4 x = 20 cos (t)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 40 cos (8 x)

y^{^{''''}} - 4 y^{^{''}} = x^{2} + 3 e^{x}

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{e ^{5 x}}{9 + x ^{2}}

y^{^{''}} + 4 y^{^{'}} + 3 = 5 sin (t)

What is the solution for y^{''}+y^'-12y=2e^{5t} ?
The solution for y^{''}+y^'-12y=2e^{5t} is y=c_{1}e^{3t}+c_{2}e^{-4t}+1/9 e^{5t}