4.14.19 \(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\)

ODE
\[ x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right ) \] ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0578267 (sec), leaf count = 75

\[\left \{\left \{y(x)\to -\frac {\sqrt {e^{5 c_1}+4 x^5}+e^{\frac {5 c_1}{2}}}{2 x^3}\right \},\left \{y(x)\to \frac {\sqrt {e^{5 c_1}+4 x^5}-e^{\frac {5 c_1}{2}}}{2 x^3}\right \}\right \}\]

Maple
cpu = 0.024 (sec), leaf count = 40

\[ \left \{ \ln \relax (x ) -{\it \_C1}+{\frac {2}{5}\ln \left (y \relax (x ) \sqrt {x}-1 \right ) }+{\frac {2}{5}\ln \left (y \relax (x ) \sqrt {x}+1 \right ) }-{\frac {2}{5}\ln \left (y \relax (x ) \sqrt {x} \right ) }=0 \right \} \] Mathematica raw input

DSolve[x*(1 + x*y[x]^2)*y'[x] == y[x]*(2 - 3*x*y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> -(E^((5*C[1])/2) + Sqrt[E^(5*C[1]) + 4*x^5])/(2*x^3)}, {y[x] -> (-E^((
5*C[1])/2) + Sqrt[E^(5*C[1]) + 4*x^5])/(2*x^3)}}

Maple raw input

dsolve(x*(1+x*y(x)^2)*diff(y(x),x) = (2-3*x*y(x)^2)*y(x), y(x),'implicit')

Maple raw output

ln(x)-_C1+2/5*ln(y(x)*x^(1/2)-1)+2/5*ln(y(x)*x^(1/2)+1)-2/5*ln(y(x)*x^(1/2)) = 0