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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} = 1, y (0) = 0, y^{^{'}} (0) = 1

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

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{2} + x

y^{^{''}} - 4 y^{^{'}} - 12 y = - 20 t + 24 t^{2}

(d^{2} - 4 d + 3) y = 2 x + 5

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