50.9.25 problem 5(a)

Internal problem ID [7961]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 5(a)
Date solved : Monday, January 27, 2025 at 03:34:08 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))}{x} \]