Internal problem ID [10292]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 95
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)
\[ y \left (x \right ) = c_{1} \operatorname {WhittakerM}\left (\frac {i n^{2}}{\sqrt {a +n}\, \sqrt {a -n}}, \frac {1}{2}, 2 i \sqrt {a +n}\, \sqrt {a -n}\, x \right ) x^{n} {\mathrm e}^{n x}+c_{2} \operatorname {WhittakerW}\left (\frac {i n^{2}}{\sqrt {a +n}\, \sqrt {a -n}}, \frac {1}{2}, 2 i \sqrt {a +n}\, \sqrt {a -n}\, x \right ) x^{n} {\mathrm e}^{n x} \]
✗ 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