What is the solution for (d^2y)/(dx^2)-4((dy)/(dx))-32y=0 ?

The solution for (d^2y)/(dx^2)-4((dy)/(dx))-32y=0 is y=c_{1}e^{8x}+c_{2}e^{-4x}

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(d^2y)/(dx^2)-4((dy)/(dx))-32y=0

\frac{d ^{2} y}{d x ^{2}} - 4 (\frac{d y}{d x}) - 32 y = 0

y = c_{1} e^{8 x} + c_{2} e^{- 4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 (\frac{d y}{d x}) - 32 y = 0

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- 4 x}

y = c_{1} e^{8 x} + c_{2} e^{- 4 x}

What is the solution for (d^2y)/(dx^2)-4((dy)/(dx))-32y=0 ?
The solution for (d^2y)/(dx^2)-4((dy)/(dx))-32y=0 is y=c_{1}e^{8x}+c_{2}e^{-4x}