88.27.3 problem 3

Internal problem ID [24233]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 226
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:01:07 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=x^{2}+1 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

Order:=6; 
ode:=diff(y(x),x)-y(x) = x^2+1; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = 1+2 x +x^{2}+\frac {2}{3} x^{3}+\frac {1}{6} x^{4}+\frac {1}{30} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 32

ode=D[y[x],{x,1}]-y[x]==1+x^2; 
ic={y[0]==1}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to \frac {x^5}{30}+\frac {x^4}{6}+\frac {2 x^3}{3}+x^2+2 x+1 \]

✓ Sympy. Time used: 0.174 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = 1 + 2 x + x^{2} + \frac {2 x^{3}}{3} + \frac {x^{4}}{6} + \frac {x^{5}}{30} + O\left (x^{6}\right ) \]