What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-30y=0 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)-30y=0 is y=c_{1}e^{6x}+c_{2}e^{-5x}

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(d^2y)/(dx^2)-(dy)/(dx)-30y=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 30 y = 0

y = c_{1} e^{6 x} + c_{2} e^{- 5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 30 y = 0

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 5 x}

y = c_{1} e^{6 x} + c_{2} e^{- 5 x}

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 2, y^{^{'}} (\frac{π}{6}) = - 4

y^{^{'''}} - 6 y^{^{''}} + 9 y^{^{'}} = 0

y^{^{'''}} - 3 y^{^{''}} + 4 y = 0

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

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

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-30y=0 ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)-30y=0 is y=c_{1}e^{6x}+c_{2}e^{-5x}