ODE
\[ \left (3 x^2-2 y(x)^2\right ) y'(x)+x y(x) y'(x)^2-6 x y(x)=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.00753407 (sec), leaf count = 49
\[\left \{\left \{y(x)\to c_1 x^2\right \},\left \{y(x)\to -\sqrt {2 c_1-3 x^2}\right \},\left \{y(x)\to \sqrt {2 c_1-3 x^2}\right \}\right \}\]
Maple ✓
cpu = 1.554 (sec), leaf count = 24
\[ \left \{ 3\,{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0,y \left ( x \right ) ={\it \_C1}\,{x}^{2} \right \} \] Mathematica raw input
DSolve[-6*x*y[x] + (3*x^2 - 2*y[x]^2)*y'[x] + x*y[x]*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*C[1]}, {y[x] -> -Sqrt[-3*x^2 + 2*C[1]]}, {y[x] -> Sqrt[-3*x^2 + 2*C[1]]}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)^2+(3*x^2-2*y(x)^2)*diff(y(x),x)-6*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x^2, 3*x^2+y(x)^2-_C1 = 0