What is the solution for (d^2y)/(dx^2)-1(dy)/(dx)-6y=0 ?

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

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(d^2y)/(dx^2)-1(dy)/(dx)-6y=0

\frac{d ^{2} y}{d x ^{2}} - 1 \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}} - 1 \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}

y^{^{''}} + 4 y^{^{'}} - 12 y = 0, y^{0} = 5, y^{^{'}} 0 = 18

y^{^{''}} + y = 0, y (π) = 1, y (0) = 0

y^{^{''''}} - 5 y^{^{'''}} + 9 y^{^{''}} - 7 y^{^{'}} + 2 y = 0

4 y^{^{''}} - 12 y^{^{'}} + 5 y = 0

y^{^{'''}} + 6 y^{^{''}} - 11 y^{^{'}} - 116 y = 0

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