59.1.3 problem 3

Internal problem ID [9175]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:51:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 65

dsolve((x^2+3)*diff(y(x),x$2)-7*x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

\[ y = 4 c_{2} \left (x^{4}-9 x^{2}+\frac {27}{8}\right ) \ln \left (\sqrt {x^{2}+3}-x \right )+\frac {5 \left (10 x^{3}-33 x \right ) c_{2} \sqrt {x^{2}+3}}{6}+\left (c_{1} +\frac {25 c_{2}}{3}\right ) \left (x^{4}-9 x^{2}+\frac {27}{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.613 (sec). Leaf size: 69

DSolve[(x^2+3)*D[y[x],{x,2}]-7*x*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} c_2 \left (3 \left (8 x^4-72 x^2+27\right ) \text {arcsinh}\left (\frac {x}{\sqrt {3}}\right )+5 x \sqrt {x^2+3} \left (33-10 x^2\right )\right )+c_1 \left (x^4-9 x^2+\frac {27}{8}\right ) \]