36.5.10 problem 11

Internal problem ID [6354]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number : 11
Date solved : Monday, January 27, 2025 at 01:58:02 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\left (x +2\right ) 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(diff(y(x),x)+(x+2)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-2 x +\frac {3}{2} x^{2}-\frac {1}{3} x^{3}-\frac {5}{24} x^{4}+\frac {3}{20} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 39

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

\[ y(x)\to c_1 \left (\frac {3 x^5}{20}-\frac {5 x^4}{24}-\frac {x^3}{3}+\frac {3 x^2}{2}-2 x+1\right ) \]