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

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

[_quadrature]

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

Mathematica
cpu = 0.00336945 (sec), leaf count = 20

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

Maple
cpu = 0.007 (sec), leaf count = 15

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

DSolve[y[x] - (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] + Log[x]}}

Maple raw input

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

Maple raw output

y(x) = ln(x)+_C1, y(x) = _C1*exp(x)