ODE
\[ x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right ) \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0366464 (sec), leaf count = 67
\[\left \{\left \{y(x)\to \frac {e^{c_1}-\sqrt {e^{2 c_1}-24 x^6}}{12 x^2}\right \},\left \{y(x)\to \frac {\sqrt {e^{2 c_1}-24 x^6}+e^{c_1}}{12 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 37
\[ \left \{ -{\frac {1}{3}\ln \left ( {\frac {{x}^{2}+6\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }+{\frac {1}{3}\ln \left ( {\frac {y \left ( x \right ) }{x}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*(x^2 - 6*y[x]^2)*y'[x] == 4*y[x]*(x^2 + 3*y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> (E^C[1] - Sqrt[E^(2*C[1]) - 24*x^6])/(12*x^2)}, {y[x] -> (E^C[1] + Sqrt[E^(2*C[1]) - 24*x^6])/(12*x^2)}}
Maple raw input
dsolve(x*(x^2-6*y(x)^2)*diff(y(x),x) = 4*(x^2+3*y(x)^2)*y(x), y(x),'implicit')
Maple raw output
-1/3*ln((x^2+6*y(x)^2)/x^2)+1/3*ln(y(x)/x)-ln(x)-_C1 = 0