What is the solution for y^{''}-4y=xsin(x) ?

The solution for y^{''}-4y=xsin(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-(xsin(x))/5-2/25 cos(x)

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y^{''}-4y=xsin(x)

y^{^{''}} - 4 y = x sin (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x sin ( x )}{5} - \frac{2}{25} cos (x)

Solution steps

y^{''} (x) - 4 y = x sin (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x sin ( x )}{5} - \frac{2}{25} cos (x)

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x sin ( x )}{5} - \frac{2}{25} cos (x)

y^{^{''}} + y^{^{'}} + 4 y = e^{x} - e^{- x}

x^{^{''}} + a x = b

y^{^{''}} - 10 y^{^{'}} + 25 y = 3 e^{5 x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{t}

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 1, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}-4y=xsin(x) ?
The solution for y^{''}-4y=xsin(x) is y=c_{1}e^{2x}+c_{2}e^{-2x}-(xsin(x))/5-2/25 cos(x)