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^{3x}+c_{2}e^{-2x}

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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^{3 x} + c_{2} e^{- 2 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^{3 x} + c_{2} e^{- 2 x}

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