60.3.309 problem 1315

Internal problem ID [11319]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1315
Date solved : Monday, January 27, 2025 at 11:11:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(x*(x^2-1)*diff(diff(y(x),x),x)+diff(y(x),x)+y(x)*a*x^3=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left (\sqrt {a}\, \sqrt {x^{2}-1}\right )+c_{2} \cos \left (\sqrt {a}\, \sqrt {x^{2}-1}\right ) \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 44

DSolve[a*x^3*y[x] + D[y[x],x] + x*(-1 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (\sqrt {a} \sqrt {x^2-1}\right )+c_2 \sin \left (\sqrt {a} \sqrt {x^2-1}\right ) \]