4.17.1 \(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\)

ODE
\[ y'(x)^2-4 (x+1) y'(x)+4 y(x)=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries], _Clairaut]

Book solution method
Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Mathematica
cpu = 0.144586 (sec), leaf count = 21

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

Maple
cpu = 0.019 (sec), leaf count = 21

\[ \left \{ y \relax (x ) = \left (1+x \right ) ^{2},y \relax (x ) =-{\frac {{\it \_C1}\, \left (-4\,x+{\it \_C1}-4 \right ) }{4}} \right \} \] Mathematica raw input

DSolve[4*y[x] - 4*(1 + x)*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(E^C[1]*(E^C[1] - 2*(1 + x)))}}

Maple raw input

dsolve(diff(y(x),x)^2-4*(1+x)*diff(y(x),x)+4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (1+x)^2, y(x) = -1/4*_C1*(-4*x+_C1-4)