What is the solution for (d^2y)/(dx^2)=9y ?

The solution for (d^2y)/(dx^2)=9y is y=c_{1}e^{3x}+c_{2}e^{-3x}

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(d^2y)/(dx^2)=9y

\frac{d ^{2} y}{d x ^{2}} = 9 y

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = 9 y

Solve linear ODE:

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

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

\frac{d}{d x} (- 4 \cdot sin^{2} (x) + 4 \cdot sin^{2} (x + \frac{π}{3}))

\frac{d}{d x} (arcsin (x^{2} - 1))

f (x) = 0.6831 x^{- 1.031}, at x = 1

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 6 x = 2 e^{- 3 t}

\frac{\partial}{\partial x} ((\frac{1}{x} + \frac{1}{y})^{- 1})

What is the solution for (d^2y)/(dx^2)=9y ?
The solution for (d^2y)/(dx^2)=9y is y=c_{1}e^{3x}+c_{2}e^{-3x}