What is the solution for (d^2y)/(dx^2)+y=e^x ?

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

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(d^2y)/(dx^2)+y=e^x

\frac{d ^{2} y}{d x ^{2}} + y = e^{x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = e^{x}

Solve linear ODE:

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

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

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