What is the solution for (d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t} ?

The solution for (d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t} is y=c_{1}e^{5t}+c_{2}e^{-2t}+(4e^{5t}t)/7

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(d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t}

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 10 y = 4 e^{5 t}

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + \frac{4 e ^{5 t} t}{7}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 10 y = 4 e^{5 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + \frac{4 e ^{5 t} t}{7}

y = c_{1} e^{5 t} + c_{2} e^{- 2 t} + \frac{4 e ^{5 t} t}{7}

y^{^{''}} - y^{^{'}} - 12 y = e^{2} x + e^{x} - 2

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2, y^{^{'}} (0) = 4

y^{^{''}} + y^{^{'}} - 12 y = \frac{e ^{x}}{x}

(6 D^{2} + 4 D + 2) y = x e^{- 2 x}

- 21 y + 4 y^{^{'}} + y^{^{''}} = t + 1

What is the solution for (d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t} ?
The solution for (d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t} is y=c_{1}e^{5t}+c_{2}e^{-2t}+(4e^{5t}t)/7