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 = 0.304775 (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 = 0.136 (sec), leaf count = 24
\[\left [y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{c \textit {\_C1}} \left (b \,x^{2}+a \right )^{\frac {c}{2 b}}}\right ]\] 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))
Maple raw output
[y(x) = exp(exp(c*_C1)*(b*x^2+a)^(1/2*c/b))]