74.17.16 problem 16

Internal problem ID [16547]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 09:10:35 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 19

Order:=6; 
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {\ln \left (x \right ) c_{2} +c_{1}}{x}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==0,y[x],{x,0,"6"-1}]
 

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