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

The solution for (y^{''}+2y^'+5)=e^{x/3} is y=c_{1}+c_{2}e^{-2x}+9/7 e^{x/3}-(5x)/2

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(y^{''}+2y^'+5)=e^{x/3}

(y^{^{''}} + 2 y^{^{'}} + 5) = e^{\frac{x}{3}}

y = c_{1} + c_{2} e^{- 2 x} + \frac{9}{7} e^{\frac{x}{3}} - \frac{5 x}{2}

Solution steps

(y^{''} (x) + 2 y^{'} (x) + 5) = e^{\frac{x}{3}}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{9}{7} e^{\frac{x}{3}} - \frac{5 x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{9}{7} e^{\frac{x}{3}} - \frac{5 x}{2}

What is the solution for (y^{''}+2y^'+5)=e^{x/3} ?
The solution for (y^{''}+2y^'+5)=e^{x/3} is y=c_{1}+c_{2}e^{-2x}+9/7 e^{x/3}-(5x)/2