What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=0 ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=0 is y=c_{1}e^{6x}+c_{2}e^{-2x}

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(d^2y)/(dx^2)-4(dy)/(dx)-12y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 2

(d^{2} + 4 d + 20)^{2} y = 0

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 6, y^{^{'}} (0) = 3

y^{^{''}} + 3 y^{^{'}} - 6 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=0 ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=0 is y=c_{1}e^{6x}+c_{2}e^{-2x}