ODE
\[ x y'(x)=a+b y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.2365 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} (\log (x)+c_1)\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 30
\[\left [y \left (x \right ) = \frac {\tan \left (\ln \left (x \right ) \sqrt {a b}+\textit {\_C1} \sqrt {a b}\right ) \sqrt {a b}}{b}\right ]\] 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))
Maple raw output
[y(x) = tan(ln(x)*(a*b)^(1/2)+_C1*(a*b)^(1/2))*(a*b)^(1/2)/b]