What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=8 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=8 is y=c_{1}e^{2x}+c_{2}e^{-x}-4

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(d^2y)/(dx^2)-(dy)/(dx)-2y=8

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 8

y = c_{1} e^{2 x} + c_{2} e^{- x} - 4

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 8

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - 4

y = c_{1} e^{2 x} + c_{2} e^{- x} - 4

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 + 3 x

y^{^{''}} + 2 y^{^{'}} + y = cos^{2} (t)

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 sin^{2} (x)

y^{^{''}} - y^{^{'}} + y = 3 sin (t)

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=8 ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=8 is y=c_{1}e^{2x}+c_{2}e^{-x}-4