ODE
\[ a+\left (x^2+1\right ) y''(x)-x y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.190339 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {1}{2} \left (-a x^2+c_1 \sqrt {x^2+1} x+c_1 \sinh ^{-1}(x)+2 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.18 (sec), leaf count = 29
\[\left [y \left (x \right ) = \textit {\_C1} \left (\frac {x \sqrt {x^{2}+1}}{2}+\frac {\arcsinh \left (x \right )}{2}\right )-\frac {a \,x^{2}}{2}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[a - x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-(a*x^2) + x*Sqrt[1 + x^2]*C[1] + ArcSinh[x]*C[1] + 2*C[2])/2}}
Maple raw input
dsolve((x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+a = 0, y(x))
Maple raw output
[y(x) = _C1*(1/2*x*(x^2+1)^(1/2)+1/2*arcsinh(x))-1/2*a*x^2+_C2]