59.1.163 problem 165

Internal problem ID [9335]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 165
Date solved : Monday, January 27, 2025 at 06:01:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 22

dsolve(9*x^2*(1+x+x^2)*diff(y(x),x$2)+3*x*(1+7*x+13*x^2)*diff(y(x),x)+(1+4*x+25*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {x^{{1}/{3}} \left (c_{2} \ln \left (x \right )+c_{1} \right )}{x^{2}+x +1} \]

✓ Solution by Mathematica

Time used: 0.294 (sec). Leaf size: 58

DSolve[9*x^2*(1+x+x^2)*D[y[x],{x,2}]+3*x*(1+7*x+13*x^2)*D[y[x],x]+(1+4*x+25*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (c_2 \log (x)+c_1) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4 K[1]+2}{K[1]^2+K[1]+1}+\frac {1}{3 K[1]}\right )dK[1]\right ) \]