4.6.34 \(a+\left (x^2+1\right ) y'(x)-x y(x)=0\)

ODE
\[ a+\left (x^2+1\right ) y'(x)-x y(x)=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.012744 (sec), leaf count = 22

\[\left \{\left \{y(x)\to c_1 \sqrt {x^2+1}-a x\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 18

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

DSolve[a - x*y[x] + (1 + x^2)*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((x^2+1)*diff(y(x),x)+a-x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (x^2+1)^(1/2)*_C1-a*x