4.11.48 \(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\)

ODE
\[ x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2 \] ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0127939 (sec), leaf count = 59

\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 25

\[ \left \{ \left (y \relax (x ) \right ) ^{2}-{\frac {{x}^{2}}{4}}-a{x}^{5}-{x}^{6}{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^2*(1 + a*x^3) + 2*x*y[x]*y'[x] == 6*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[x^2 + 4*a*x^5 + 4*x^6*C[1]]/2}, {y[x] -> Sqrt[x^2 + 4*a*x^5 + 4*
x^6*C[1]]/2}}

Maple raw input

dsolve(2*x*y(x)*diff(y(x),x)+x^2*(a*x^3+1) = 6*y(x)^2, y(x),'implicit')

Maple raw output

y(x)^2-1/4*x^2-a*x^5-x^6*_C1 = 0