What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=18 ?

The solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=18 is y=c_{1}e^{2x}+c_{2}e^{-3x}-3

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(d^2y)/(dx^2)+(dy)/(dx)-6y=18

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 18

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 18

Solve linear ODE:

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

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

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

y^{^{''}} + 49 y = sec (7 x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x) + x e^{3 x}

y^{^{''}} - y^{^{'}} - 2 y = 10 sin (2 x)

y^{^{''}} - 7 y^{^{'}} + 12 y = 4 e^{2 x}

What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=18 ?
The solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=18 is y=c_{1}e^{2x}+c_{2}e^{-3x}-3