Internal problem ID [10090]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2 Equations Containing Power
Functions. page 213
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-a \,x^{n -2} \left (x^{n} a +n +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 113
dsolve(diff(y(x),x$2)-a*x^(n-2)*(a*x^n+n+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{n} a}{n}} x +c_{2} \left (\left (\left (n^{2}-n \right ) x^{\frac {1}{2}-\frac {3 n}{2}}+2 a n \,x^{\frac {1}{2}-\frac {n}{2}}\right ) \WhittakerM \left (\frac {-1-n}{2 n}, -\frac {1}{2 n}+1, \frac {2 x^{n} a}{n}\right )+x^{\frac {1}{2}-\frac {3 n}{2}} \WhittakerM \left (\frac {n -1}{2 n}, -\frac {1}{2 n}+1, \frac {2 x^{n} a}{n}\right ) \left (n -1\right )^{2}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]-a*x^(n-2)*(a*x^n+n+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved