4.17.36 \(2 y'(x)^2-(1-x) y'(x)-y(x)=0\)

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

Book solution method
Clairaut’s equation and related types, main form

Mathematica
cpu = 0.00254165 (sec), leaf count = 15

\[\left \{\left \{y(x)\to c_1 \left (2 c_1+x-1\right )\right \}\right \}\]

Maple
cpu = 0.019 (sec), leaf count = 22

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (2\,{\it \_C1}+x-1 \right ) ,y \relax (x ) =-{\frac { \left (-1+x \right ) ^{2}}{8}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> C[1]*(-1 + x + 2*C[1])}}

Maple raw input

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

Maple raw output

y(x) = -1/8*(-1+x)^2, y(x) = _C1*(2*_C1+x-1)