What is the solution for 3y^{''}-y=e^x-5 ?

The solution for 3y^{''}-y=e^x-5 is y=c_{1}e^{x/(sqrt(3))}+c_{2}e^{-x/(sqrt(3))}+1/2 e^x+5

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3y^{''}-y=e^x-5

3 y^{^{''}} - y = e^{x} - 5

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{1}{2} e^{x} + 5

Solution steps

3 y^{''} (x) - y = e^{x} - 5

Solve linear ODE:

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{1}{2} e^{x} + 5

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{1}{2} e^{x} + 5

What is the solution for 3y^{''}-y=e^x-5 ?
The solution for 3y^{''}-y=e^x-5 is y=c_{1}e^{x/(sqrt(3))}+c_{2}e^{-x/(sqrt(3))}+1/2 e^x+5