4.17.26 \(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\)

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

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Use new variable

Mathematica
cpu = 0.0510093 (sec), leaf count = 59

\[\left \{\left \{y(x)\to \frac {-4 c_1 x+4 c_1^2+x^2-1}{x-2 c_1}\right \},\left \{y(x)\to \frac {4 c_1 x+4 c_1^2+x^2-1}{2 c_1+x}\right \}\right \}\]

Maple
cpu = 0.036 (sec), leaf count = 79

\[ \left \{ 4+ \left (y \relax (x ) \right ) ^{2}=0,x-\int ^{y \relax (x ) }\!2\, \left ({{\it \_a}}^{2}-\sqrt {{{\it \_a}}^{2} \left ({{\it \_a}}^{2}+4 \right ) }+4 \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \relax (x ) }\!2\, \left ({{\it \_a}}^{2}+\sqrt {{{\it \_a}}^{2} \left ({{\it \_a}}^{2}+4 \right ) }+4 \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-1 + x^2 - 4*x*C[1] + 4*C[1]^2)/(x - 2*C[1])}, {y[x] -> (-1 + x^2 + 4
*x*C[1] + 4*C[1]^2)/(x + 2*C[1])}}

Maple raw input

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

Maple raw output

4+y(x)^2 = 0, x-Intat(2/(_a^2-(_a^2*(_a^2+4))^(1/2)+4),_a = y(x))-_C1 = 0, x-Int
at(2/(_a^2+(_a^2*(_a^2+4))^(1/2)+4),_a = y(x))-_C1 = 0