ODE
\[ \left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.17112 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \},\{y(x)\to -\log (x)+c_1\}\right \}\]
Maple ✓
cpu = 0.046 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\ln \left (x \right )+\textit {\_C1}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x^{2}}{2}}\right ]\] 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))
Maple raw output
[y(x) = -ln(x)+_C1, y(x) = _C1*exp(1/2*x^2)]