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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int sin^{2} (4 x) d x

\frac{d}{d y} (10 y - y^{2})

\frac{\partial}{\partial y} (x^{y - 1})

x (\frac{d y}{d x}) + 2 y = 3

\frac{d y}{d x} y = 7^{x}

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