18.2.12 problem Problem 15.23

Internal problem ID [3495]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.23
Date solved : Monday, January 27, 2025 at 07:39:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 45

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

\[ y(x)\to \frac {6 c_1 x^3+3 c_2 x-4 c_2}{6 \sqrt {2-x} (x-2)^{3/2} x} \]