What is the solution for y^{''}+y= 3/2 sin(x) ?

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

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y^{''}+y= 3/2 sin(x)

y^{^{''}} + y = \frac{3}{2} sin (x)

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

Solution steps

y^{''} (x) + y = \frac{3}{2} sin (x)

Solve linear ODE:

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

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

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