44.17.7 problem 1(d) solving using series

Internal problem ID [9364]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 1(d) solving using series
Date solved : Tuesday, September 30, 2025 at 06:17:49 PM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 47

Order:=8; 
ode:=diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\frac {1}{720} x^{6}-\frac {1}{5040} x^{7}\right ) y \left (0\right )+O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 53

ode=D[y[x],x]+y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to c_1 \left (-\frac {x^7}{5040}+\frac {x^6}{720}-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=8)
 

\[ y{\left (x \right )} = C_{1} - C_{1} x + \frac {C_{1} x^{2}}{2} - \frac {C_{1} x^{3}}{6} + \frac {C_{1} x^{4}}{24} - \frac {C_{1} x^{5}}{120} + \frac {C_{1} x^{6}}{720} - \frac {C_{1} x^{7}}{5040} + O\left (x^{8}\right ) \]