4.18.6 $-(x^2+1)y^{\prime }(x)+x{y}^{\prime }(x{)}^2+x=0$

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

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.00480235 (sec), leaf count = 24

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

Maple ✓
cpu = 0.006 (sec), leaf count = 18

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

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

Mathematica raw output

{{y[x] -> x^2/2 + C[1]}, {y[x] -> C[1] + Log[x]}}

Maple raw input

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

Maple raw output

y(x) = 1/2*x^2+_C1, y(x) = ln(x)+_C1