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 = 0.155288 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {x^2}{2}+c_1\right \},\{y(x)\to \log (x)+c_1\}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {x^{2}}{2}+\textit {\_C1}, y \left (x \right ) = \ln \left (x \right )+\textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x^2+_C1, y(x) = ln(x)+_C1]