4.18.6 \(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\)

ODE
\[ -\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

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

\[\left \{\left \{y(x)\to c_1+\frac {x^2}{2}\right \},\left \{y(x)\to c_1+\log (x)\right \}\right \}\]

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

\[ \left \{ y \relax (x ) ={\frac {{x}^{2}}{2}}+{\it \_C1},y \relax (x ) =\ln \relax (x ) +{\it \_C1} \right \} \] 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