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 = 0.0234863 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \frac {1}{2} c_1 \sqrt {x^2-1} x-\frac {1}{2} c_1 \log \left (\sqrt {x^2-1}+x\right )+c_2+x\right \}\right \}\]
Maple ✓
cpu = 0.037 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) =-{\frac {1}{2} \left ( -2\,\sqrt {1+x} \left ( x+{\it \_C2} \right ) \sqrt {-1+x}+ \left ( -{x}^{3}+\ln \left ( x+\sqrt {{x}^{2}-1} \right ) \sqrt { \left ( -1+x \right ) \left ( 1+x \right ) }+x \right ) {\it \_C1} \right ) {\frac {1}{\sqrt {-1+x}}}{\frac {1}{\sqrt {1+x}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/2/(1+x)^(1/2)/(-1+x)^(1/2)*(-2*(1+x)^(1/2)*(x+_C2)*(-1+x)^(1/2)+(-x^3+ln(x+(x^2-1)^(1/2))*((-1+x)*(1+x))^(1/2)+x)*_C1)