ODE
\[ 4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0 \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.344704 (sec), leaf count = 85
\[\left \{\left \{y(x)\to -\frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1^2}}{2 a}\right \},\left \{y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1^2}}{2 a}\right \}\right \}\]
Maple ✓
cpu = 0.821 (sec), leaf count = 63
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax=0,[x \left ( {\it \_T} \right ) ={\frac {1}{4\,a} \left ( \left ( {{\it \_C1}}^{2}+4\,{a}^{2} \right ) \sqrt {{{\it \_T}}^{2}+1}-4\,{\it \_C1}\,{\it \_T}\,a \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) ={{\it \_C1}{\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \] Mathematica raw input
DSolve[4*a^2 - 4*a*x + y[x]^2 - 4*a*y[x]*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[16*a^3*x - 4*a^2*x^2 - 4*a*x*C[1] - C[1]^2]/(2*a)}, {y[x] -> Sqrt[16*a^3*x - 4*a^2*x^2 - 4*a*x*C[1] - C[1]^2]/(2*a)}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2-4*a*y(x)*diff(y(x),x)+4*a^2-4*a*x+y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x)^2-4*a*x = 0, [x(_T) = 1/4*((_C1^2+4*a^2)*(_T^2+1)^(1/2)-4*_C1*_T*a)/(_T^2+1)^(1/2)/a, y(_T) = _C1/(_T^2+1)^(1/2)]