60.3.229 problem 1234

Internal problem ID [11239]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1234
Date solved : Monday, January 27, 2025 at 10:49:40 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.340 (sec). Leaf size: 59

dsolve((x^2-1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+2=0,y(x), singsol=all)
 

\[ y = -\int -\frac {-2 \sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x -1}\, \sqrt {x +1}+c_{1} \left (x^{2}-1\right )}{\left (x -1\right )^{{3}/{2}} \left (x +1\right )^{{3}/{2}}}d x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 31

DSolve[2 + x*D[y[x],x] + (-1 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2-\frac {1}{4} \left (-2 \log \left (\sqrt {x^2-1}+x\right )+c_1\right ){}^2 \]