What is the solution for y^{''}-y^'=e^xsin(x) ?

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

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y^{''}-y^'=e^xsin(x)

y^{^{''}} - y^{^{'}} = e^{x} sin (x)

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

Solution steps

y^{''} (x) - y^{'} (x) = e^{x} sin (x)

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} - 3 y = cos (2 x)

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 20 e^{3 t}

y^{^{''}} - 8 y^{^{'}} + 17 y = 10 e^{4 x} sec (x)

y^{^{''}} - 4 y = 12

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

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