What is the solution for linear (d^2y)/(dx^2)+(dy)/(dx)-6y=0 ?

The solution for linear (d^2y)/(dx^2)+(dy)/(dx)-6y=0 is y=c_{1}e^{2x}+c_{2}e^{-3x}

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linear (d^2y)/(dx^2)+(dy)/(dx)-6y=0

linear

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

y = c_{1} e^{2 x} + c_{2} e^{- 3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x}

- 2 y^{^{''}} + 5 y^{^{'}} + 10 y = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 2, y^{^{'}} (0) = 16

100 y^{^{''}} + 180 y^{^{'}} + 145 y = 0

y^{^{''}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = - 3

(D^{2} + 64)^{2} y = 0

What is the solution for linear (d^2y)/(dx^2)+(dy)/(dx)-6y=0 ?
The solution for linear (d^2y)/(dx^2)+(dy)/(dx)-6y=0 is y=c_{1}e^{2x}+c_{2}e^{-3x}