78.3.6 problem 2.a

Internal problem ID [21002]
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 : 2.a
Date solved : Thursday, October 02, 2025 at 07:01:18 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=y-x \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)-x; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 29

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

\[ y(x)\to \frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+2 x+2 \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - 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)
 

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