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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- x} sin (x) + x e^{3 x}

y^{^{''}} - 2 y^{^{'}} = 1, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - y^{^{'}} + 14 y = 5 + e^{\frac{x}{2}}

y^{^{''}} - 16 y = 9.6 e^{4 x} + 30 e^{x}

y^{^{''}} - y = 3 e^{2 x}

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