What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=6+4t ?

The solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=6+4t is y=c_{1}e^{5t}+c_{2}e^{-3t}-(4t)/(15)-82/225

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(d^2y)/(dt^2)-2(dy)/(dt)-15y=6+4t

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 6 + 4 t

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{4 t}{15} - \frac{82}{225}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 6 + 4 t

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{4 t}{15} - \frac{82}{225}

y = c_{1} e^{5 t} + c_{2} e^{- 3 t} - \frac{4 t}{15} - \frac{82}{225}

5 y^{^{''}} + y = sin (2 x) + x

(4 D^{2} + 4 D + 1) y = x e^{- \frac{x}{2}} sin (x)

y^{^{''}} + 2 y^{^{'}} + 4 y = 111 e^{2 x} cos (3 x)

y^{^{''''}} - 4 y^{^{''}} = x^{2} + e^{x}

y^{^{''}} + 9 y = 5 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=6+4t ?
The solution for (d^2y)/(dt^2)-2(dy)/(dt)-15y=6+4t is y=c_{1}e^{5t}+c_{2}e^{-3t}-(4t)/(15)-82/225