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

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

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

\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}

\frac{d}{d x} (\frac{x - y}{2 x + 4 y})

y - 3 ln (x) - 4 = 0

\int e^{7 x + 6} d x

7 x + 11 (2.5)

\frac{d}{d x} f (x) = \frac{2}{x ^{2}} - 5 x

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