4.7.44 \(x (a x+1) y'(x)+a-y(x)=0\)

ODE
\[ x (a x+1) y'(x)+a-y(x)=0 \] ODE Classification

[_separable]

Book solution method
Linear ODE

Mathematica
cpu = 0.0086965 (sec), leaf count = 19

\[\left \{\left \{y(x)\to \frac {a+c_1 x}{a x+1}\right \}\right \}\]

Maple
cpu = 0.016 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}\,x+a}{ax+1}} \right \} \] Mathematica raw input

DSolve[a - y[x] + x*(1 + a*x)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (a + x*C[1])/(1 + a*x)}}

Maple raw input

dsolve(x*(a*x+1)*diff(y(x),x)+a-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C1*x+a)/(a*x+1)