ODE
\[ \left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.191007 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {-\log (\cos (x))+c_1}{x^2+1}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {-\ln \left (\cos \left (x \right )\right )+\textit {\_C1}}{x^{2}+1}\right ]\] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == Tan[x] - 2*x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1] - Log[Cos[x]])/(1 + x^2)}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = tan(x)-2*x*y(x), y(x))
Maple raw output
[y(x) = (-ln(cos(x))+_C1)/(x^2+1)]