7.13.1 problem 1

Internal problem ID [400]
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 : 1
Date solved : Saturday, March 29, 2025 at 04:52:50 PM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 37

ode=D[y[x],x]==y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.635 (sec). Leaf size: 37

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=6)
 

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