ODE
\[ \sqrt {x^2+1} y'(x)=2 x-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.276111 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^{-\sinh ^{-1}(x)} \left (x^2+\sqrt {x^2+1} x-\sinh ^{-1}(x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {x^{2}+x \sqrt {x^{2}+1}-\arcsinh \left (x \right )+\textit {\_C1}}{x +\sqrt {x^{2}+1}}\right ]\] Mathematica raw input
DSolve[Sqrt[1 + x^2]*y'[x] == 2*x - y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^2 + x*Sqrt[1 + x^2] - ArcSinh[x] + C[1])/E^ArcSinh[x]}}
Maple raw input
dsolve(diff(y(x),x)*(x^2+1)^(1/2) = 2*x-y(x), y(x))
Maple raw output
[y(x) = (x^2+x*(x^2+1)^(1/2)-arcsinh(x)+_C1)/(x+(x^2+1)^(1/2))]