What is the solution for y^{''}+12y^'+35y=70t^2+48t+4+48e^t ?

The solution for y^{''}+12y^'+35y=70t^2+48t+4+48e^t is y=c_{1}e^{-5t}+c_{2}e^{-7t}+2t^2+e^t

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y^{''}+12y^'+35y=70t^2+48t+4+48e^t

y^{^{''}} + 12 y^{^{'}} + 35 y = 70 t^{2} + 48 t + 4 + 48 e^{t}

y = c_{1} e^{- 5 t} + c_{2} e^{- 7 t} + 2 t^{2} + e^{t}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 35 y = 70 t^{2} + 48 t + 4 + 48 e^{t}

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} e^{- 7 t} + 2 t^{2} + e^{t}

y = c_{1} e^{- 5 t} + c_{2} e^{- 7 t} + 2 t^{2} + e^{t}

h (t) = - 5 t^{2}

\frac{d}{d x} (\frac{5 sin ( x )}{3 + cos ( x )})

\int_{0}^{\frac{5}{2}} \frac{1}{25 + 4 x ^{2}} d x

\int 3 x^{2} - 12 x + 12 d x

\int_{1}^{4} (2 x + x) d x

What is the solution for y^{''}+12y^'+35y=70t^2+48t+4+48e^t ?
The solution for y^{''}+12y^'+35y=70t^2+48t+4+48e^t is y=c_{1}e^{-5t}+c_{2}e^{-7t}+2t^2+e^t