Internal problem ID [11310]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x^{2}-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 89
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)
\[ y \left (x \right ) = {\mathrm e}^{x n} x^{n} \left (\operatorname {WhittakerM}\left (\frac {i n^{2}}{\sqrt {a -n}\, \sqrt {a +n}}, \frac {1}{2}, 2 i \sqrt {a -n}\, \sqrt {a +n}\, x \right ) c_{1} +\operatorname {WhittakerW}\left (\frac {i n^{2}}{\sqrt {a -n}\, \sqrt {a +n}}, \frac {1}{2}, 2 i \sqrt {a -n}\, \sqrt {a +n}\, x \right ) c_{2} \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*y''[x]-2*n*x*(1+x)*y'[x]+(n^2+n+a^2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved