59.1.10 problem 10

Internal problem ID [9182]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:51:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve((x^2-6*x+10)*diff(y(x),x$2)-4*(x-3)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x^{3}+c_{2} x^{2}+6 \left (-5 c_{1} -c_{2} \right ) x +60 c_{1} +\frac {26 c_{2}}{3} \]

✓ Solution by Mathematica

Time used: 0.314 (sec). Leaf size: 84

DSolve[(x^2-6*x+10)*D[y[x],{x,2}]-4*(x-3)*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-6 x+10\right ) \exp \left (\int _1^x\frac {K[1]-(3-3 i)}{(K[1]-6) K[1]+10}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {K[1]-(3-3 i)}{(K[1]-6) K[1]+10}dK[1]\right )dK[2]+c_1\right ) \]