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

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 = 0.00344913 (sec), leaf count = 28

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

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

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

Maple raw output

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