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

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

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(x^2-9)/x (dy)/(dx)+y=0

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

y = \frac{c _{1}}{x ^{2} - 9}

Solution steps

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

Solve separable ODE:

y = \frac{c _{1}}{x ^{2} - 9}

y = \frac{c _{1}}{x ^{2} - 9}

(x y + x) d x = (x^{2} y^{2} + x^{2} + y^{2} + 1) d y, y (1) = 2

\frac{d y}{d x} = - \frac{3}{7} x^{9} y^{8}

2 y^{^{'}} = y^{2} - 6 y + 9

\frac{d v}{d t} = 6 - 8 v

\frac{d y}{d x} + y = y^{- \frac{1}{2}}

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