What is the solution for y^{''}-2y^'+5y=e^xsin(x) ?

The solution for y^{''}-2y^'+5y=e^xsin(x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/3 e^xsin(x)

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y^{''}-2y^'+5y=e^xsin(x)

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

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{3} e^{x} sin (x)

Solution steps

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

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{3} e^{x} sin (x)

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{3} e^{x} sin (x)

\int_{0}^{\infty} 1 d x

\int e^{- s t} - t e^{- s t} d t

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

\int_{- \infty}^{0} \frac{1}{5 - 6 x} d x

\int_{1}^{2} \frac{5 - x}{x ^{3}} d x

What is the solution for y^{''}-2y^'+5y=e^xsin(x) ?
The solution for y^{''}-2y^'+5y=e^xsin(x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/3 e^xsin(x)