ODE
\[ \left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0115811 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_1+\sin (x)}{x^2-1}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\frac {\sin \left ( x \right ) +{\it \_C1}}{{x}^{2}-1}} \right \} \] Mathematica raw input
DSolve[Cos[x] + (1 - x^2)*y'[x] == 2*x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + Sin[x])/(-1 + x^2)}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x)+cos(x) = 2*x*y(x), y(x),'implicit')
Maple raw output
y(x) = (sin(x)+_C1)/(x^2-1)