ODE
\[ \left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.513509 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {a^2-x^2+c_1{}^2}{2 c_1}\right \}\right \}\]
Maple ✓
cpu = 3.783 (sec), leaf count = 51
\[\left [y \left (x \right ) = \sqrt {a^{2}-x^{2}}, y \left (x \right ) = -\sqrt {a^{2}-x^{2}}, y \left (x \right ) = x^{2} \textit {\_C1} -\textit {\_C1} \,a^{2}-\frac {1}{4 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[x^2 + 2*x*y[x]*y'[x] + (a^2 - x^2)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (a^2 - x^2 + C[1]^2)/(2*C[1])}}
Maple raw input
dsolve((a^2-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+x^2 = 0, y(x))
Maple raw output
[y(x) = (a^2-x^2)^(1/2), y(x) = -(a^2-x^2)^(1/2), y(x) = x^2*_C1-_C1*a^2-1/4/_C1]