What is the solution for y^{''}-36y=6e^2x ?

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

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y^{''}-36y=6e^2x

y^{^{''}} - 36 y = 6 e^{2} x

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

Solution steps

y^{''} (x) - 36 y = 6 e^{2} x

Solve linear ODE:

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

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

- x^{^{''}} + x = 4

y^{^{''}} - y^{^{'}} - 2 y - 3 = - 6 x

d (a sin (t)) = d x

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 6 - e^{x} + e^{4 x}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}, y (0) = 18

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