What is the solution for 9y^{''}+30y^'+25y=2x+5 ?

The solution for 9y^{''}+30y^'+25y=2x+5 is y=c_{1}e^{-(5x)/3}+c_{2}e^{-(5x)/3}x+(2x)/(25)+13/125

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9y^{''}+30y^'+25y=2x+5

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 2 x + 5

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- \frac{5 x}{3}} x + \frac{2 x}{25} + \frac{13}{125}

Solution steps

9 y^{''} (x) + 30 y^{'} (x) + 25 y = 2 x + 5

Solve linear ODE:

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- \frac{5 x}{3}} x + \frac{2 x}{25} + \frac{13}{125}

y = c_{1} e^{- \frac{5 x}{3}} + c_{2} e^{- \frac{5 x}{3}} x + \frac{2 x}{25} + \frac{13}{125}

y^{^{''}} + 11 y^{^{'}} + 5 y = 48 e^{2 x}

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

y^{^{''}} + y^{^{'}} - 2 y = 3 e^{2 x}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{2 x} - 2

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- x}

What is the solution for 9y^{''}+30y^'+25y=2x+5 ?
The solution for 9y^{''}+30y^'+25y=2x+5 is y=c_{1}e^{-(5x)/3}+c_{2}e^{-(5x)/3}x+(2x)/(25)+13/125