59.1.596 problem 612

Internal problem ID [9768]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 612
Date solved : Monday, January 27, 2025 at 06:14:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 31

dsolve(3*x^2*(3+x)*diff(y(x),x$2)-x*(15+x)*diff(y(x),x)-20*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (x^{2}-36 x -243\right )+\frac {c_{2} \left (7 x +27\right )}{\left (x +3\right )^{{1}/{3}}}}{x^{{2}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.494 (sec). Leaf size: 123

DSolve[3*x^2*(3+x)*D[y[x],{x,2}]-x*(15+x)*D[y[x],x]-20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{7} (7 x+27) \exp \left (\int _1^x\left (\frac {1}{3 K[1]+9}-\frac {3}{2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x-\frac {K[2]+15}{3 K[2]^2+9 K[2]}dK[2]\right ) \left (c_2 \int _1^x\frac {49 \exp \left (-2 \int _1^{K[3]}\left (\frac {1}{3 K[1]+9}-\frac {3}{2 K[1]}\right )dK[1]\right )}{(7 K[3]+27)^2}dK[3]+c_1\right ) \]