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 = 0.15994 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -\frac {1}{4} c_1 (-4 x-4+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 25
\[\left [y \left (x \right ) = x^{2}+2 x +1, y \left (x \right ) = x \textit {\_C1} -\frac {1}{4} \textit {\_C1}^{2}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[4*y[x] - 4*(1 + x)*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/4*(C[1]*(-4 - 4*x + C[1]))}}
Maple raw input
dsolve(diff(y(x),x)^2-4*(x+1)*diff(y(x),x)+4*y(x) = 0, y(x))
Maple raw output
[y(x) = x^2+2*x+1, y(x) = x*_C1-1/4*_C1^2+_C1]