What is the solution for y^{''}+5y^'+6y=-10te^{2t} ?

The solution for y^{''}+5y^'+6y=-10te^{2t} is y=c_{1}e^{-2t}+c_{2}e^{-3t}-(e^{2t}t)/2+9/40 e^{2t}

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y^{''}+5y^'+6y=-10te^{2t}

y^{^{''}} + 5 y^{^{'}} + 6 y = - 10 t e^{2 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} - \frac{e ^{2 t} t}{2} + \frac{9}{40} e^{2 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = - 10 t e^{2 t}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} - \frac{e ^{2 t} t}{2} + \frac{9}{40} e^{2 t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} - \frac{e ^{2 t} t}{2} + \frac{9}{40} e^{2 t}

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What is the solution for y^{''}+5y^'+6y=-10te^{2t} ?
The solution for y^{''}+5y^'+6y=-10te^{2t} is y=c_{1}e^{-2t}+c_{2}e^{-3t}-(e^{2t}t)/2+9/40 e^{2t}