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^{4x}+c_{2}e^{-2x}

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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^{4 x} + c_{2} e^{- 2 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^{4 x} + c_{2} e^{- 2 x}

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

\int \frac{9}{x - 4} d x

\frac{d}{d x} (tan (4 x^{5}))

\int_{0}^{1} \frac{1}{x - 2} d x

x \to 2 lim (x^{2} x)

f (x) = \frac{x}{( 5 x - 9 ) ^{5}}

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^{4x}+c_{2}e^{-2x}