What is the solution for x(dy)/(dx)-(1-x^2)y=0 ?

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

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x(dy)/(dx)-(1-x^2)y=0

x \frac{d y}{d x} - (1 - x^{2}) y = 0

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

Solution steps

x \frac{d y}{d x} - (1 - x^{2}) y = 0

Solve separable ODE:

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

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

y^{^{'}} = x y^{\frac{1}{2}}, y (0) = \frac{1}{16} x^{4}

e^{x} (\frac{d y}{d x}) = 1 + y^{2}

\frac{d y}{d x} = 4 x 36 - y^{2}

\frac{d y}{d t} = \frac{- t}{y}, y = 4

y = sin (2) (ln (x^{2} - 3 x + 2)) y^{^{'}}

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