ODE
\[ -x \left (x^2-2 y(x)^2\right )-2 y(x)^3 y'(x)+x y(x)^2 y'(x)^2=0 \] ODE Classification
[_separable]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.252111 (sec), leaf count = 73
\[\left \{\left \{y(x)\to -\sqrt {x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {x^2+2 c_1}\right \},\left \{y(x)\to -\sqrt {x^2+c_1 x^4}\right \},\left \{y(x)\to \sqrt {x^2+c_1 x^4}\right \}\right \}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 52
\[\left [y \left (x \right ) = \sqrt {x^{2}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {x^{2}+\textit {\_C1}}, y \left (x \right ) = \sqrt {x^{2} \textit {\_C1} +1}\, x, y \left (x \right ) = -\sqrt {x^{2} \textit {\_C1} +1}\, x\right ]\] Mathematica raw input
DSolve[-(x*(x^2 - 2*y[x]^2)) - 2*y[x]^3*y'[x] + x*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[x^2 + 2*C[1]]}, {y[x] -> Sqrt[x^2 + 2*C[1]]}, {y[x] -> -Sqrt[x^2 + x^4*C[1]]}, {y[x] -> Sqrt[x^2 + x^4*C[1]]}}
Maple raw input
dsolve(x*y(x)^2*diff(y(x),x)^2-2*y(x)^3*diff(y(x),x)-x*(x^2-2*y(x)^2) = 0, y(x))
Maple raw output
[y(x) = (x^2+_C1)^(1/2), y(x) = -(x^2+_C1)^(1/2), y(x) = (_C1*x^2+1)^(1/2)*x, y(x) = -(_C1*x^2+1)^(1/2)*x]