78.3.1 problem 1.a

Internal problem ID [20997]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 4, Series solutions. Problems section 4.9
Problem number : 1.a
Date solved : Thursday, October 02, 2025 at 07:01:16 PM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

Order:=5; 
ode:=diff(y(x),x) = y(x); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = 2+2 x +x^{2}+\frac {1}{3} x^{3}+\frac {1}{12} x^{4}+\operatorname {O}\left (x^{5}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 25

ode=D[y[x],x]==y[x]; 
ic={y[0]==2}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,4}]
 

\[ y(x)\to \frac {x^4}{12}+\frac {x^3}{3}+x^2+2 x+2 \]

✓ Sympy. Time used: 0.115 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = 2 + 2 x + x^{2} + \frac {x^{3}}{3} + \frac {x^{4}}{12} + \frac {x^{5}}{60} + O\left (x^{6}\right ) \]