4.7.43 \(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\)

ODE
\[ \left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x)) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0180848 (sec), leaf count = 28

\[\left \{\left \{y(x)\to e^{e^{c_1} \left (a+b x^2\right )^{\frac {c}{2 b}}}\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 27

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

DSolve[(a + b*x^2)*y'[x] == c*x*Log[y[x]]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> E^(E^C[1]*(a + b*x^2)^(c/(2*b)))}}

Maple raw input

dsolve((b*x^2+a)*diff(y(x),x) = c*x*y(x)*ln(y(x)), y(x),'implicit')

Maple raw output

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