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]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
dsolve((1-x^2)*diff(y(x),x$2)+x*diff(y(x),x)=1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}+c_{1} \left (\frac {\sqrt {x -1}\, \left (x +1\right )^{\frac {3}{2}}}{2}-\frac {\sqrt {x -1}\, \sqrt {x +1}}{2}-\frac {\sqrt {\left (x +1\right ) \left (x -1\right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{2 \sqrt {x +1}\, \sqrt {x -1}}\right )+c_{2} \]
✓ 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]
\[ y(x)\to \frac {1}{2} \left (-2 c_1 \text {arctanh}\left (\frac {\sqrt {x^2-1}}{x-1}\right )+x^2+c_1 \sqrt {x^2-1} x+2 c_2\right ) \]