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

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

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y^{''}+y=4xcos(x)

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

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