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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int \frac{2 x}{x} d x

\int 1 + 2 cos (x) + cos^{2} (x) d x

y = x^{3}, y = x^{2}

\frac{\partial}{\partial t} (t^{2} + 1)

f (x) = \frac{( x ^{2} )}{x - 5}

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