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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - a y (x) = 0

Solve linear ODE:

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

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

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

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} + 6 y = 0

(D^{2} + 1) y = 0

2 \frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 18 y = 0

2 x^{^{''}} + 4 x^{^{'}} - 3 x = 0

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