59.1.544 problem 560

Internal problem ID [9716]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 560
Date solved : Monday, January 27, 2025 at 06:13:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$2)-x*(5-x)*diff(y(x),x)+(9-4*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \left (-c_{2} {\mathrm e}^{-x}+\left (\operatorname {Ei}_{1}\left (x \right ) c_{2} +c_{1} \right ) \left (x +1\right )\right ) x^{3} \]

✓ Solution by Mathematica

Time used: 0.501 (sec). Leaf size: 72

DSolve[x^2*D[y[x],{x,2}]-x*(5-x)*D[y[x],x]+(9-4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (x+1) \left (c_2 \int _1^x\frac {e^{-K[2]-1}}{K[2] (K[2]+1)^2}dK[2]+c_1\right ) \exp \left (\frac {1}{2} \left (-\int _1^x\left (1-\frac {5}{K[1]}\right )dK[1]+x+1\right )\right ) \]