4.7.12 \(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\)

ODE
\[ \left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0 \] ODE Classification

[_separable]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0363504 (sec), leaf count = 33

\[\left \{\left \{y(x)\to -\frac {e^{c_1}}{b e^{c_1}-\sqrt {a^2+x^2}}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 21

\[ \left \{ -\sqrt {{a}^{2}+{x}^{2}}{\it \_C1}+ \left (y \relax (x ) \right ) ^{-1}+b=0 \right \} \] Mathematica raw input

DSolve[x*y[x] + b*x*y[x]^2 + (a^2 + x^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(E^C[1]/(b*E^C[1] - Sqrt[a^2 + x^2]))}}

Maple raw input

dsolve((a^2+x^2)*diff(y(x),x)+x*y(x)+b*x*y(x)^2 = 0, y(x),'implicit')

Maple raw output

-(a^2+x^2)^(1/2)*_C1+1/y(x)+b = 0