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

ODE
\[ x^2 y'(x)=a+b y(x)^2 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0220567 (sec), leaf count = 39

\[\left \{\left \{y(x)\to -\frac {\sqrt {a} \tan \left (\frac {\sqrt {a} \sqrt {b} \left (1-c_1 x\right )}{x}\right )}{\sqrt {b}}\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 27

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

DSolve[x^2*y'[x] == a + b*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -((Sqrt[a]*Tan[(Sqrt[a]*Sqrt[b]*(1 - x*C[1]))/x])/Sqrt[b])}}

Maple raw input

dsolve(x^2*diff(y(x),x) = a+b*y(x)^2, y(x),'implicit')

Maple raw output

-1/x-1/(a*b)^(1/2)*arctan(y(x)*b/(a*b)^(1/2))+_C1 = 0