59.1.180 problem 182

Internal problem ID [9352]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 182
Date solved : Monday, January 27, 2025 at 06:01:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 45

dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(6+11*x)*diff(y(x),x)+(6+32*x)*y(x)=0,y(x), singsol=all)
 

\[ y = 3 c_{1} x^{8}+14 c_{1} x^{7}+21 c_{1} x^{6}+35 c_{2} x^{4}+42 c_{2} x^{3}+21 c_{2} x^{2}+4 c_{2} x \]

✓ Solution by Mathematica

Time used: 0.528 (sec). Leaf size: 122

DSolve[x^2*(1+x)*D[y[x],{x,2}]-x*(6+11*x)*D[y[x],x]+(6+32*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} (3 x-4) \exp \left (\int _1^x\left (\frac {7}{2 (K[1]+1)}-\frac {2}{K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (-\frac {5}{K[2]+1}-\frac {6}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {9 \exp \left (-2 \int _1^{K[3]}\frac {3 K[1]-4}{2 K[1] (K[1]+1)}dK[1]\right )}{(4-3 K[3])^2}dK[3]+c_1\right ) \]