60.3.120 problem 1124

Internal problem ID [11130]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1124
Date solved : Tuesday, January 28, 2025 at 05:41:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.161 (sec). Leaf size: 29

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

\[ y = c_{1} \operatorname {KummerM}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right )+c_{2} \operatorname {KummerU}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 65

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

\[ y(x)\to c_1 \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},a+\frac {1}{2},x^2\right )+i^{1-2 a} c_2 x^{1-2 a} \operatorname {Hypergeometric1F1}\left (-a-\frac {n}{2}+\frac {1}{2},\frac {3}{2}-a,x^2\right ) \]