ODE
\[ a+\left (x^2+1\right ) y'(x)-x y(x)=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.169655 (sec), leaf count = 22
\[\left \{\left \{y(x)\to -a x+c_1 \sqrt {x^2+1}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 18
\[\left [y \left (x \right ) = \sqrt {x^{2}+1}\, \textit {\_C1} -a x\right ]\] 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))
Maple raw output
[y(x) = (x^2+1)^(1/2)*_C1-a*x]