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 = 0.171273 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \frac {c_1}{x}\right \},\left \{y(x)\to -\sqrt {x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 31
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}, y \left (x \right ) = \sqrt {x^{2}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {x^{2}+\textit {\_C1}}\right ]\] 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] -> C[1]/x}, {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) = 1/x*_C1, y(x) = (x^2+_C1)^(1/2), y(x) = -(x^2+_C1)^(1/2)]