What is the solution for (d^2y)/(dx^2)-y=4e^xcos(x) ?

The solution for (d^2y)/(dx^2)-y=4e^xcos(x) is y=c_{1}e^x+c_{2}e^{-x}+8/5 e^xsin(x)-4/5 e^xcos(x)

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(d^2y)/(dx^2)-y=4e^xcos(x)

\frac{d ^{2} y}{d x ^{2}} - y = 4 e^{x} cos (x)

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{8}{5} e^{x} sin (x) - \frac{4}{5} e^{x} cos (x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = 4 e^{x} cos (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{8}{5} e^{x} sin (x) - \frac{4}{5} e^{x} cos (x)

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{8}{5} e^{x} sin (x) - \frac{4}{5} e^{x} cos (x)

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

y^{^{''}} + 2 y^{^{'}} + 4 y = 2 t - 3 cos (2 t)

3 y^{^{''}} - 9 y^{^{'}} = sin (2 x)

y^{^{''}} + 9 y = 3, y (0) = 0, y^{^{'}} (0) = 0

8 y^{^{''}} + 7 y^{^{'}} - y = 17

What is the solution for (d^2y)/(dx^2)-y=4e^xcos(x) ?
The solution for (d^2y)/(dx^2)-y=4e^xcos(x) is y=c_{1}e^x+c_{2}e^{-x}+8/5 e^xsin(x)-4/5 e^xcos(x)