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

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

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

y^{^{''}} + y = 4 x \cdot 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 \cdot 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)

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{1.5 e ^{5 t}}{t ^{2} + 1}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 12 y = 3 cos (x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 2 e^{2 x}

y^{^{''}} - 3 y^{^{'}} = 1 + e^{x} + cos (x) + sin (x)

4 y^{^{''}} - 2 y^{^{'}} = 7

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