ODE
\[ \sqrt {x^2+1} y'(x)=2 x-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0303187 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^{-\sinh ^{-1}(x)} \left (c_1+x^2+\sqrt {x^2+1} x-\sinh ^{-1}(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={1 \left ( {x}^{2}+x\sqrt {{x}^{2}+1}-{\it Arcsinh} \left ( x \right ) +{\it \_C1} \right ) \left ( x+\sqrt {{x}^{2}+1} \right ) ^{-1}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (x^2+x*(x^2+1)^(1/2)-arcsinh(x)+_C1)/(x+(x^2+1)^(1/2))