ODE
\[ \left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.167573 (sec), leaf count = 47
\[\left \{\{y(x)\to c_1 x\},\left \{y(x)\to -\sqrt {-x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {-x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.092 (sec), leaf count = 33
\[\left [y \left (x \right ) = x \textit {\_C1}, y \left (x \right ) = \sqrt {-x^{2}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {-x^{2}+\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-(x*y[x]) + (x^2 - y[x]^2)*y'[x] + x*y[x]*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1]}, {y[x] -> -Sqrt[-x^2 + 2*C[1]]}, {y[x] -> Sqrt[-x^2 + 2*C[1]]}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)^2+(x^2-y(x)^2)*diff(y(x),x)-x*y(x) = 0, y(x))
Maple raw output
[y(x) = x*_C1, y(x) = (-x^2+_C1)^(1/2), y(x) = -(-x^2+_C1)^(1/2)]