59.1.95 problem 97

Internal problem ID [9267]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 97
Date solved : Monday, January 27, 2025 at 06:00:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 27

dsolve(6*x^2*diff(y(x),x$2)+x*(10-x)*diff(y(x),x)-(2+x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{{5}/{6}}+c_{1} \operatorname {WhittakerM}\left (-\frac {1}{6}, \frac {2}{3}, \frac {x}{6}\right ) {\mathrm e}^{\frac {x}{12}} x}{x^{{11}/{6}}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 38

DSolve[6*x^2*D[y[x],{x,2}]+x*(10-x)*D[y[x],x]-(2+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \sqrt [3]{x} L_{-\frac {4}{3}}^{\frac {4}{3}}\left (\frac {x}{6}\right )+\frac {6 \sqrt [3]{6} c_1}{x} \]