4.18.28 \((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\)

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

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.0040427 (sec), leaf count = 21

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

Maple
cpu = 0.007 (sec), leaf count = 16

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{x}},y \relax (x ) ={\it \_C1}\,{{\rm e}^{x}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> E^x*C[1]}, {y[x] -> C[1]/x}}

Maple raw input

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

Maple raw output

y(x) = _C1/x, y(x) = _C1*exp(x)