ODE
\[ 3 x^3+2 (3 x+1) x y(x) y'(x)+4 y(x)^2 y'(x)^2=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.0086825 (sec), leaf count = 81
\[\left \{\left \{y(x)\to -\sqrt {2 c_1-x^3}\right \},\left \{y(x)\to \sqrt {2 c_1-x^3}\right \},\left \{y(x)\to -\sqrt {2 c_1-\frac {x^2}{2}}\right \},\left \{y(x)\to \sqrt {2 c_1-\frac {x^2}{2}}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 29
\[ \left \{ {x}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0, \left ( y \left ( x \right ) \right ) ^{2}+{\frac {{x}^{2}}{2}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[3*x^3 + 2*x*(1 + 3*x)*y[x]*y'[x] + 4*y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-x^3 + 2*C[1]]}, {y[x] -> Sqrt[-x^3 + 2*C[1]]}, {y[x] -> -Sqrt[-x^2/2 + 2*C[1]]}, {y[x] -> Sqrt[-x^2/2 + 2*C[1]]}}
Maple raw input
dsolve(4*y(x)^2*diff(y(x),x)^2+2*(1+3*x)*x*y(x)*diff(y(x),x)+3*x^3 = 0, y(x),'implicit')
Maple raw output
y(x)^2+1/2*x^2-_C1 = 0, x^3+y(x)^2-_C1 = 0