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

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

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

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

y = \frac{e ^{\frac{- 1 + c _{1} x}{x}}}{x}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{\frac{- 1 + c _{1} x}{x}}}{x}

y = \frac{e ^{\frac{- 1 + c _{1} x}{x}}}{x}

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

2 x tan (y) d x + sec^{2} (y) d y = 0

y^{^{'}} = e^{x} cos^{2} (y), y (0) = \frac{π}{4}

\frac{d y}{d x} = - \frac{3}{2} y + \frac{1}{2} y^{2}

a d a + b d b = 0

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