20.1.19 problem Problem 25

Internal problem ID [3576]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 25
Date solved : Monday, January 27, 2025 at 07:45:23 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_2 \log (x)+c_1}{x^2} \]