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 = 0.17793 (sec), leaf count = 81
\[\left \{\left \{y(x)\to -\sqrt {-x^3+2 c_1}\right \},\left \{y(x)\to \sqrt {-x^3+2 c_1}\right \},\left \{y(x)\to -\sqrt {-\frac {x^2}{2}+2 c_1}\right \},\left \{y(x)\to \sqrt {-\frac {x^2}{2}+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 59
\[\left [y \left (x \right ) = -\frac {\sqrt {-2 x^{2}+4 \textit {\_C1}}}{2}, y \left (x \right ) = \frac {\sqrt {-2 x^{2}+4 \textit {\_C1}}}{2}, y \left (x \right ) = \sqrt {-x^{3}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {-x^{3}+\textit {\_C1}}\right ]\] 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[-1/2*x^2 + 2*C[1]]}, {y[x] -> Sqrt[-1/2*x^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))
Maple raw output
[y(x) = -1/2*(-2*x^2+4*_C1)^(1/2), y(x) = 1/2*(-2*x^2+4*_C1)^(1/2), y(x) = (-x^3+_C1)^(1/2), y(x) = -(-x^3+_C1)^(1/2)]