ODE
\[ \left (1-x^2\right ) y''(x)+x y'(x)=x \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.188318 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {1}{2} c_1 \sqrt {x^2-1} x-\frac {1}{2} c_1 \log \left (\sqrt {x^2-1}+x\right )+x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.153 (sec), leaf count = 65
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \sqrt {x -1}\, \left (x +1\right )^{\frac {3}{2}}}{2}-\frac {\sqrt {x -1}\, \sqrt {x +1}\, \textit {\_C1}}{2}-\frac {\textit {\_C1} \sqrt {\left (x -1\right ) \left (x +1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{2 \sqrt {x +1}\, \sqrt {x -1}}+x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[x*y'[x] + (1 - x^2)*y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> x + (x*Sqrt[-1 + x^2]*C[1])/2 + C[2] - (C[1]*Log[x + Sqrt[-1 + x^2]])/2}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x) = x, y(x))
Maple raw output
[y(x) = 1/2*_C1*(x-1)^(1/2)*(x+1)^(3/2)-1/2*(x-1)^(1/2)*(x+1)^(1/2)*_C1-1/2*_C1*((x-1)*(x+1))^(1/2)/(x+1)^(1/2)/(x-1)^(1/2)*ln(x+(x^2-1)^(1/2))+x+_C2]