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

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

\[ \left \{ x-{1\arctan \left ({by \relax (x ) {\frac {1}{\sqrt {ab}}}} \right ) {\frac {1}{\sqrt {ab}}}}+{\it \_C1}=0 \right \} \] 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