ODE
\[ x (a+y(x))^2 y'(x)=b y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.417532 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {$\#$1}}+2 a \log (\text {$\#$1})+\text {$\#$1}\& \right ][b \log (x)+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.31 (sec), leaf count = 33
\[[y \left (x \right ) = {\mathrm e}^{\RootOf \left (\ln \left (x \right ) b \,{\mathrm e}^{\textit {\_Z}}+\textit {\_C1} b \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}}+a^{2}\right )}]\] Mathematica raw input
DSolve[x*(a + y[x])^2*y'[x] == b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[2*a*Log[#1] - a^2/#1 + #1 & ][C[1] + b*Log[x]]}}
Maple raw input
dsolve(x*(a+y(x))^2*diff(y(x),x) = b*y(x)^2, y(x))
Maple raw output
[y(x) = exp(RootOf(ln(x)*b*exp(_Z)+_C1*b*exp(_Z)-2*_Z*a*exp(_Z)-exp(2*_Z)+a^2))]