59.1.580 problem 596

Internal problem ID [9752]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 596
Date solved : Monday, January 27, 2025 at 06:13:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x^2*(4+3*x)*diff(y(x),x$2)-x*(4-3*x)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {x \left (c_{2} \ln \left (x \right )+c_{1} \right )}{3 x +4} \]

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 49

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

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