4.14.38 \(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\)

ODE
\[ x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0 \] ODE Classification

[[_homogeneous, `class A`], _rational, _dAlembert]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0653655 (sec), leaf count = 209

\[\left \{\left \{y(x)\to -\frac {\sqrt {-\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}-4 x^2}}{2 \sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}-4 x^2}}{2 \sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}-4 x^2}}{2 \sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {8 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}-4 x^2}}{2 \sqrt {2}}\right \}\right \}\]

Maple
cpu = 0.024 (sec), leaf count = 43

\[ \left \{ {\frac {1}{2}\ln \left ({\frac {{x}^{2}+ \left (y \relax (x ) \right ) ^{2}}{{x}^{2}}} \right ) }-\ln \left ({\frac {{x}^{2}+2\, \left (y \relax (x ) \right ) ^{2}}{{x}^{2}}} \right ) -\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^3 + y[x]*(3*x^2 + 2*y[x]^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[E^(2*C[1]) - 4*x^2 - Sqrt[E^(4*C[1]) + 8*E^(2*C[1])*x^2]]/(2*Sqr
t[2])}, {y[x] -> Sqrt[E^(2*C[1]) - 4*x^2 - Sqrt[E^(4*C[1]) + 8*E^(2*C[1])*x^2]]/
(2*Sqrt[2])}, {y[x] -> -Sqrt[E^(2*C[1]) - 4*x^2 + Sqrt[E^(4*C[1]) + 8*E^(2*C[1])
*x^2]]/(2*Sqrt[2])}, {y[x] -> Sqrt[E^(2*C[1]) - 4*x^2 + Sqrt[E^(4*C[1]) + 8*E^(2
*C[1])*x^2]]/(2*Sqrt[2])}}

Maple raw input

dsolve((3*x^2+2*y(x)^2)*y(x)*diff(y(x),x)+x^3 = 0, y(x),'implicit')

Maple raw output

1/2*ln((x^2+y(x)^2)/x^2)-ln((x^2+2*y(x)^2)/x^2)-ln(x)-_C1 = 0