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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to + 3 lim ((\frac{x - 1}{2 x - 4})^{\frac{1}{x - 3}})

y^{^{''}} = - 4 \cdot y

\int \frac{1}{16 e ^{- 3 x} + e ^{3 x}} d x

y = x e^{x}

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 4)^{7})

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