60.3.268 problem 1273

Internal problem ID [11278]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1273
Date solved : Tuesday, January 28, 2025 at 05:57:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 17

dsolve(4*x^2*diff(diff(y(x),x),x)-(-4*k*x+4*m^2+x^2-1)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {WhittakerM}\left (k , m , x\right )+c_{2} \operatorname {WhittakerW}\left (k , m , x\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

DSolve[(1 - 4*m^2 + 4*k*x - x^2)*y[x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 M_{k,m}(x)+c_2 W_{k,m}(x) \]