4.18.29 $(1-x^{2}y(x))y^{\prime }(x)+x{y}^{\prime }(x{)}^2-xy(x)=0$

ODE
$$(1-x^{2}y(x))y^{\prime }(x)+x{y}^{\prime }(x{)}^2-xy(x)=0$$ ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.00344913 (sec), leaf count = 28

$$\{\{y(x)\to c_1{e}^{\frac{x^2}{2}}\},\{y(x)\to c_1-\log (x)\}\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 21

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{x^2}{2}},y\left(x\right)=-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}\}$$ Mathematica raw input

DSolve[-(x*y[x]) + (1 - x^2*y[x])*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(x^2/2)*C[1]}, {y[x] -> C[1] - Log[x]}}

Maple raw input

dsolve(x*diff(y(x),x)^2+(1-x^2*y(x))*diff(y(x),x)-x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = -ln(x)+_C1, y(x) = _C1*exp(1/2*x^2)