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

The solution for y^{''}-2y^'+5y=sin(x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/5 sin(x)+1/10 cos(x)

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

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

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

Solution steps

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

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

y^{^{''}} + 4 y = 4 sec^{2} (2 t)

y^{^{''}} - 2 y^{^{'}} + y = 10 e^{- 2 x} cos (x)

y^{^{''}} - y = sinh (x)

4 y^{^{''}} - y = e^{\frac{x}{2}} + 9

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

What is the solution for y^{''}-2y^'+5y=sin(x) ?
The solution for y^{''}-2y^'+5y=sin(x) is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/5 sin(x)+1/10 cos(x)