What is the solution for y^{''}+2y^'+y=64e^{(7t)} ?

The solution for y^{''}+2y^'+y=64e^{(7t)} is y=c_{1}e^{-t}+c_{2}te^{-t}+e^{7t}

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y^{''}+2y^'+y=64e^{(7t)}

y^{^{''}} + 2 y^{^{'}} + y = 64 e^{(7 t)}

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{7 t}

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 64 e^{(7 t)}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{7 t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{7 t}

\frac{d}{d x} ((x - 3)^{- 2})

\frac{\partial}{\partial x} (\frac{2 x}{2 y})

3^{x^{2}}

y^{^{'}} = \frac{3 sec ( y )}{( x - 4 ) ^{2}}

\int_{1}^{\infty} \frac{x}{x ^{2} + 4} d x

What is the solution for y^{''}+2y^'+y=64e^{(7t)} ?
The solution for y^{''}+2y^'+y=64e^{(7t)} is y=c_{1}e^{-t}+c_{2}te^{-t}+e^{7t}