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 = 0.277794 (sec), leaf count = 59
\[\left \{\left \{y(x)\to \frac {x^2-4 c_1 x-1+4 c_1{}^2}{x-2 c_1}\right \},\left \{y(x)\to \frac {x^2+4 c_1 x-1+4 c_1{}^2}{x+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.097 (sec), leaf count = 83
\[\left [y \left (x \right ) = -2 i, y \left (x \right ) = 2 i, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\frac {\textit {\_a}^{2}}{2}+2-\frac {\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}}{2}}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\frac {\textit {\_a}^{2}}{2}+2+\frac {\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}}{2}}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] 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))
Maple raw output
[y(x) = -2*I, y(x) = 2*I, x-Intat(1/(1/2*_a^2+2-1/2*(_a^2*(_a^2+4))^(1/2)),_a = y(x))-_C1 = 0, x-Intat(1/(1/2*_a^2+2+1/2*(_a^2*(_a^2+4))^(1/2)),_a = y(x))-_C1 = 0]