ODE
\[ x y'(x)=a+b y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0210846 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} \left (c_1+\log (x)\right )\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 24
\[ \left \{ \ln \left ( x \right ) -{1\arctan \left ( {by \left ( x \right ) {\frac {1}{\sqrt {ab}}}} \right ) {\frac {1}{\sqrt {ab}}}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == a + b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[a]*Tan[Sqrt[a]*Sqrt[b]*(C[1] + Log[x])])/Sqrt[b]}}
Maple raw input
dsolve(x*diff(y(x),x) = a+b*y(x)^2, y(x),'implicit')
Maple raw output
ln(x)-1/(a*b)^(1/2)*arctan(y(x)*b/(a*b)^(1/2))+_C1 = 0