59.1.179 problem 181

Internal problem ID [9351]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 181
Date solved : Monday, January 27, 2025 at 06:01:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 62

dsolve(x^2*(1+2*x)*diff(y(x),x$2)-2*x*(3+14*x)*diff(y(x),x)+(6+100*x)*y(x)=0,y(x), singsol=all)
 

\[ y = 8 c_{2} x^{10}+36 c_{2} x^{9}+72 c_{2} x^{8}+84 c_{2} x^{7}+63 c_{2} x^{6}+2016 c_{1} x^{5}+672 c_{1} x^{4}+144 c_{1} x^{3}+18 c_{1} x^{2}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.282 (sec). Leaf size: 105

DSolve[x^2*(1+2*x)*D[y[x],{x,2}]-2*x*(3+14*x)*D[y[x],x]+(6+100*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {10}{2 K[1]+1}-\frac {2}{K[1]}\right )dK[1]-\frac {1}{2} \int _1^x-\frac {28 K[2]+6}{2 K[2]^2+K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\left (\frac {10}{2 K[1]+1}-\frac {2}{K[1]}\right )dK[1]\right )dK[3]+c_1\right ) \]