What is the solution for y^{''}+2y=e^x+2 ?

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

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y^{''}+2y=e^x+2

y^{^{''}} + 2 y = e^{x} + 2

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

Solution steps

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

Solve linear ODE:

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

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

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