Internal problem ID [2286]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve((1-x^2)*diff(y(x),x$2)+x*diff(y(x),x)=1,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {-\sqrt {x +1}\, \left (x^{2}+2 c_{2} \right ) \sqrt {x -1}+c_{1} \left (-x^{3}+\sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right )+x \right )}{2 \sqrt {x -1}\, \sqrt {x +1}} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 50
DSolve[(1-x^2)*y''[x]+x*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (-2 c_1 \text {arctanh}\left (\frac {\sqrt {x^2-1}}{x-1}\right )+x^2+c_1 \sqrt {x^2-1} x+2 c_2\right ) \]