What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-24y=4e^{6t} ?

The solution for (d^2y)/(dt^2)-2(dy)/(dt)-24y=4e^{6t} is y=c_{1}e^{6t}+c_{2}e^{-4t}+(2e^{6t}t)/5

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(d^2y)/(dt^2)-2(dy)/(dt)-24y=4e^{6t}

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 24 y = 4 e^{6 t}

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} + \frac{2 e ^{6 t} t}{5}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 24 y = 4 e^{6 t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} + \frac{2 e ^{6 t} t}{5}

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} + \frac{2 e ^{6 t} t}{5}

y^{^{''}} - y^{^{'}} = cos (x) + 4 e^{- x}

5 y^{^{''}} + y^{^{'}} = - 4 x, y (0) = 0

x^{^{''}} + 2 x = 1

x^{^{''}} + 2 x = 6

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 2 y = 2 x^{2} - 3 x + 6

What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-24y=4e^{6t} ?
The solution for (d^2y)/(dt^2)-2(dy)/(dt)-24y=4e^{6t} is y=c_{1}e^{6t}+c_{2}e^{-4t}+(2e^{6t}t)/5