7.13.6 problem 6

Internal problem ID [405]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:53:25 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 37

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

\[ y = \left (1+\frac {1}{2} x +\frac {1}{4} x^{2}+\frac {1}{8} x^{3}+\frac {1}{16} x^{4}+\frac {1}{32} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 41

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

\[ y(x)\to c_1 \left (\frac {x^5}{32}+\frac {x^4}{16}+\frac {x^3}{8}+\frac {x^2}{4}+\frac {x}{2}+1\right ) \]