What is the solution for (d^2y)/(dx^2)-9y=0 ?

The solution for (d^2y)/(dx^2)-9y=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}

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(d^2y)/(dx^2)-9y=0

\frac{d ^{2} y}{d x ^{2}} - 9 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 9 y = 0

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{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

x \to 2 lim (2 x^{2} - x + 2)

(x - y) d x + (x) d y = 0

y^{^{'}} + 3 y = e^{2 x} + 1

\int 2 (2 + x^{2})^{\frac{3}{2}} x d x

What is the solution for (d^2y)/(dx^2)-9y=0 ?
The solution for (d^2y)/(dx^2)-9y=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}