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

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

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y^{''}+y=2cos(x)+x

y^{^{''}} + y = 2 cos (x) + x

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

Solution steps

y^{''} (x) + y = 2 cos (x) + x

Solve linear ODE:

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

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

- 3 y^{^{''}} - 2 y^{^{'}} + y = t^{2} + t - 2 e^{2 t}

x^{^{'''}} - 4 x^{^{''}} + 5 x^{^{'}} - 2 x = 2 t + 3

y^{^{''}} + 4 y = sin (2 x + 3)

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

y^{^{''}} + y^{^{'}} - 12 y = - 40 t + 24 t^{2}

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