4.20.28 \(4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0\)

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 = 0.489202 (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 = 1.77 (sec), leaf count = 113

\[\left [y \left (x \right ) = -2 \sqrt {a x}, y \left (x \right ) = 2 \sqrt {a x}, y \left (x \right ) = -\frac {\sqrt {-16 a^{4}+32 a^{3} x -16 a^{2} x^{2}+8 \textit {\_C1} \,a^{2}+8 \textit {\_C1} a x -\textit {\_C1}^{2}}}{4 a}, y \left (x \right ) = \frac {\sqrt {-16 a^{4}+32 a^{3} x -16 a^{2} x^{2}+8 \textit {\_C1} \,a^{2}+8 \textit {\_C1} a x -\textit {\_C1}^{2}}}{4 a}\right ]\] 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] -> -1/2*Sqrt[16*a^3*x - 4*a^2*x^2 - 4*a*x*C[1] - C[1]^2]/a}, {y[x] -> Sqr
t[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))

Maple raw output

[y(x) = -2*(a*x)^(1/2), y(x) = 2*(a*x)^(1/2), y(x) = -1/4*(-16*a^4+32*a^3*x-16*a
^2*x^2+8*_C1*a^2+8*_C1*a*x-_C1^2)^(1/2)/a, y(x) = 1/4*(-16*a^4+32*a^3*x-16*a^2*x
^2+8*_C1*a^2+8*_C1*a*x-_C1^2)^(1/2)/a]