What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-8y=0 ?

The solution for (d^2y)/(dx^2)+2(dy)/(dx)-8y=0 is y=c_{1}e^{2x}+c_{2}e^{-4x}

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(d^2y)/(dx^2)+2(dy)/(dx)-8y=0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 8 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 8 y = 0

Solve linear ODE:

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

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

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

16 y^{^{''}} - 40 y^{^{'}} + 25 y = 0, y (0) = 3, y (0) = - \frac{9}{4}

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = 7, y^{^{'}} (0) = 4

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

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

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-8y=0 ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)-8y=0 is y=c_{1}e^{2x}+c_{2}e^{-4x}