4.18.34 \(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\)

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

[_rational, _dAlembert]

Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Mathematica
cpu = 2.70518 (sec), leaf count = 2

\[\{\{\}\}\]

Maple
cpu = 0.034 (sec), leaf count = 54

\[ \left \{ [x \left ({\it \_T} \right ) ={\frac {\ln \left ({\it \_T}+1 \right ) + \left ({\it \_T}+1 \right ) ^{-1}+{\it \_C1}}{{{\it \_T}}^{2}}},y \left ({\it \_T} \right ) ={\frac { \left (2\,{\it \_T}+2 \right ) \ln \left ({\it \_T}+1 \right ) + \left (2\,{\it \_C1}+1 \right ) {\it \_T}+2\,{\it \_C1}+2}{{\it \_T}\, \left ({\it \_T}+1 \right ) }}] \right \} \] Mathematica raw input

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

Mathematica raw output

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Maple raw input

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

Maple raw output

[x(_T) = 1/_T^2*(ln(_T+1)+1/(_T+1)+_C1), y(_T) = ((2*_T+2)*ln(_T+1)+(2*_C1+1)*_T
+2*_C1+2)/_T/(_T+1)]