30.13.10 problem 11

Internal problem ID [7642]
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 : Tuesday, September 30, 2025 at 04:55:24 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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

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

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

ode=D[y[x],x]+(x+2)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.178 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

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