ODE
\[ x y'(x)=a x^2+b y(x)^2+y(x) \] ODE Classification
[[_homogeneous, `class D`], _rational, _Riccati]
Book solution method
Riccati ODE, Special cases
Mathematica ✓
cpu = 0.260208 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {\sqrt {a} x \tan \left (\sqrt {a} \sqrt {b} (x+c_1)\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 30
\[\left [y \left (x \right ) = \frac {\tan \left (\textit {\_C1} \sqrt {a b}+x \sqrt {a b}\right ) x \sqrt {a b}}{b}\right ]\] Mathematica raw input
DSolve[x*y'[x] == a*x^2 + y[x] + b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[a]*x*Tan[Sqrt[a]*Sqrt[b]*(x + C[1])])/Sqrt[b]}}
Maple raw input
dsolve(x*diff(y(x),x) = a*x^2+y(x)+b*y(x)^2, y(x))
Maple raw output
[y(x) = tan(_C1*(a*b)^(1/2)+x*(a*b)^(1/2))*x*(a*b)^(1/2)/b]