62.32.9 problem Ex 9

Internal problem ID [12986]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 9
Date solved : Tuesday, January 28, 2025 at 08:24:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 85

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

\[ y = {\mathrm e}^{n x} x^{n} \left (\operatorname {WhittakerM}\left (\frac {i n^{2}}{\sqrt {a +n}\, \sqrt {a -n}}, \frac {1}{2}, 2 i \sqrt {a +n}\, \sqrt {a -n}\, x \right ) c_{1} +\operatorname {WhittakerW}\left (\frac {i n^{2}}{\sqrt {a +n}\, \sqrt {a -n}}, \frac {1}{2}, 2 i \sqrt {a +n}\, \sqrt {a -n}\, x \right ) c_{2} \right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved