What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-12y=24 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)-12y=24 is y=c_{1}e^{2x}+c_{2}e^{-6x}-2

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(d^2y)/(dx^2)+4(dy)/(dx)-12y=24

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 y = 24

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 y = 24

Solve linear ODE:

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

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

y^{^{''}} + y = 3 x sin (x)

x^{^{''}} + 6 x^{^{'}} + 25 x = t e^{- t}

y^{^{''}} + 9 y = 2 sec (3 x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- x} - sin (2 x)

y^{^{''}} - 2 y^{^{'}} + y = t^{2} - 1

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-12y=24 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)-12y=24 is y=c_{1}e^{2x}+c_{2}e^{-6x}-2