ODE
\[ y'(x)=a+b y(x)^2 \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.0198322 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} \left (c_1+x\right )\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 23
\[ \left \{ x-{1\arctan \left ( {by \left ( x \right ) {\frac {1}{\sqrt {ab}}}} \right ) {\frac {1}{\sqrt {ab}}}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x] == a + b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[a]*Tan[Sqrt[a]*Sqrt[b]*(x + C[1])])/Sqrt[b]}}
Maple raw input
dsolve(diff(y(x),x) = a+b*y(x)^2, y(x),'implicit')
Maple raw output
x-1/(a*b)^(1/2)*arctan(y(x)*b/(a*b)^(1/2))+_C1 = 0