What is the solution for (d^2y)/(dx^2)-36y=0 ?

The solution for (d^2y)/(dx^2)-36y=0 is y=c_{1}e^{6x}+c_{2}e^{-6x}

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(d^2y)/(dx^2)-36y=0

\frac{d ^{2} y}{d x ^{2}} - 36 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 36 y = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} = 0

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (0) = 4

6 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

y^{^{''}} + \frac{4}{3} y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{16}{3}

What is the solution for (d^2y)/(dx^2)-36y=0 ?
The solution for (d^2y)/(dx^2)-36y=0 is y=c_{1}e^{6x}+c_{2}e^{-6x}