What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)-64y=0 ?

The solution for (d^2y)/(dx^2)-12(dy)/(dx)-64y=0 is y=c_{1}e^{16x}+c_{2}e^{-4x}

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(d^2y)/(dx^2)-12(dy)/(dx)-64y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} - 64 y = 0

y = c_{1} e^{16 x} + c_{2} e^{- 4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} - 64 y = 0

Solve linear ODE:

y = c_{1} e^{16 x} + c_{2} e^{- 4 x}

y = c_{1} e^{16 x} + c_{2} e^{- 4 x}

\frac{10}{32} y^{^{''}} + \frac{1}{6} y = 0, y (0) = \frac{1}{6}, y^{^{'}} (0) = - 1

10000 y^{^{''}} - 729 y = 0, y (0) = 9

y^{^{''}} + 16 y = 0, y (π^{8}) = - 4, y^{^{'}} (π^{8}) = - 8

y^{^{''}} = - y, y (0) = 0

y^{^{''}} = 13 \cdot y

What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)-64y=0 ?
The solution for (d^2y)/(dx^2)-12(dy)/(dx)-64y=0 is y=c_{1}e^{16x}+c_{2}e^{-4x}