59.1.89 problem 91

Internal problem ID [9261]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 91
Date solved : Monday, January 27, 2025 at 06:00:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 30

dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 56

DSolve[3*x^2*D[y[x],{x,2}]+x*(1+x)*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\frac {1}{3} (-x-1)} \left (c_2 x^{2/3}-3 \sqrt [3]{3 e} c_1 (-x)^{2/3} \Gamma \left (\frac {4}{3},-\frac {x}{3}\right )\right )}{x} \]