What is the solution for y^{''}+y=x+e^x ?

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

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y^{''}+y=x+e^x

y^{^{''}} + y = x + e^{x}

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

Solution steps

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

Solve linear ODE:

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

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

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