What is the solution for x^2y-3xy^'-2y=0 ?

The solution for x^2y-3xy^'-2y=0 is y=(e^{(x^2+c_{1})/6})/(x^{2/3)}

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x^2y-3xy^'-2y=0

x^{2} y - 3 x y^{^{'}} - 2 y = 0

y = \frac{e ^{\frac{x ^{2} + c _{1}}{6}}}{x ^{\frac{2}{3}}}

Solution steps

x^{2} y - 3 x y^{'} (x) - 2 y = 0

Solve separable ODE:

y = \frac{e ^{\frac{x ^{2} + c _{1}}{6}}}{x ^{\frac{2}{3}}}

y = \frac{e ^{\frac{x ^{2} + c _{1}}{6}}}{x ^{\frac{2}{3}}}

sin (x) d x + \frac{1}{y} d y = 0, y (0) = 0

\frac{d y}{d x} = x^{8} y^{- 5}, y (0) = 2

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

\frac{d y}{d x} = a (500 - y)

\frac{f ^{^{'}} ( x )}{f ( x )} = \frac{2}{x}

What is the solution for x^2y-3xy^'-2y=0 ?
The solution for x^2y-3xy^'-2y=0 is y=(e^{(x^2+c_{1})/6})/(x^{2/3)}