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

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

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