ODE
\[ \left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.175907 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 20
\[\left [y \left (x \right ) = \frac {x^{2}}{3}+\frac {1}{3}+\frac {\textit {\_C1}}{\sqrt {x^{2}+1}}\right ]\] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == x*(1 + x^2) - x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (1 + x^2)/3 + C[1]/Sqrt[1 + x^2]}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = x*(x^2+1)-x*y(x), y(x))
Maple raw output
[y(x) = 1/3*x^2+1/3+1/(x^2+1)^(1/2)*_C1]