61.33.6 problem 244

Internal problem ID [12744]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number : 244
Date solved : Tuesday, January 28, 2025 at 08:23:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 2.751 (sec). Leaf size: 137

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

\[ y = x^{-\frac {a}{2}-\frac {1}{2}+\frac {n}{2}} {\mathrm e}^{\frac {b \,x^{-n +2}}{2 n -4}} \left (\operatorname {WhittakerM}\left (\frac {\left (-b +2\right ) a -2+b \left (n -1\right )}{2 b \left (n -2\right )}, \frac {a -1}{2 n -4}, \frac {b \,x^{-n +2}}{n -2}\right ) c_{1} +\operatorname {WhittakerW}\left (\frac {\left (-b +2\right ) a -2+b \left (n -1\right )}{2 b \left (n -2\right )}, \frac {a -1}{2 n -4}, \frac {b \,x^{-n +2}}{n -2}\right ) c_{2} \right ) \]

✗ Solution by Mathematica

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

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

Not solved