What is the solution for y^{''}+y=3xcos(x) ?

The solution for y^{''}+y=3xcos(x) is y=c_{1}cos(x)+c_{2}sin(x)+(3x^2sin(x))/4+(3xcos(x))/4

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y^{''}+y=3xcos(x)

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

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3 x ^{2} sin ( x )}{4} + \frac{3 x cos ( x )}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3 x ^{2} sin ( x )}{4} + \frac{3 x cos ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{3 x ^{2} sin ( x )}{4} + \frac{3 x cos ( x )}{4}

y^{^{'''}} - 2 y^{^{'}} - y^{^{'}} + 2 y = (x + 1)^{2}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = e^{3 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{1}{1 + e ^{x}}

2 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 6 y = 3 e^{2 x}

y^{^{''}} - 4 y^{^{'}} = cosh (2 x)

What is the solution for y^{''}+y=3xcos(x) ?
The solution for y^{''}+y=3xcos(x) is y=c_{1}cos(x)+c_{2}sin(x)+(3x^2sin(x))/4+(3xcos(x))/4