What is the solution for 36y^{''}-y=(xe^x)/6 ?

The solution for 36y^{''}-y=(xe^x)/6 is y=c_{1}e^{x/6}+c_{2}e^{-x/6}+(e^xx)/(210)-12/1225 e^x

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36y^{''}-y=(xe^x)/6

36 y^{^{''}} - y = \frac{x e ^{x}}{6}

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}

Solution steps

36 y^{''} (x) - y = \frac{x e ^{x}}{6}

Solve linear ODE:

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}

y^{^{''}} - 5 y^{^{'}} - 50 y = 5 + 3 t

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

2 y^{^{''}} + y = 9 e^{2 t}

y^{^{''}} + 6 y = cos (7 t)

(d^{2} + 144) (d^{2} - 144) 2 (d + 12) 4 x = 144

What is the solution for 36y^{''}-y=(xe^x)/6 ?
The solution for 36y^{''}-y=(xe^x)/6 is y=c_{1}e^{x/6}+c_{2}e^{-x/6}+(e^xx)/(210)-12/1225 e^x