4.13.48 \(x (a+y(x))^2 y'(x)=b y(x)^2\)

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 = 0.0569887 (sec), leaf count = 32

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {$\#$1}}+2 a \log (\text {$\#$1})+\text {$\#$1}\& \right ]\left [b \log (x)+c_1\right ]\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 34

\[ \left \{ \ln \relax (x ) -{\frac {y \relax (x ) }{b}}+{\frac {{a}^{2}}{by \relax (x ) }}-2\,{\frac {a\ln \left (y \relax (x ) \right ) }{b}}+{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

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