4.14.16 problem 19

Internal problem ID [1398]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:33:35 AM
CAS classification : [_separable]

\begin{align*} \left (1-x \right ) y^{\prime }&=y \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

Order:=6; 
ode:=(1-x)*diff(y(x),x) = y(x); 
dsolve(ode,y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 21

ode=(1-x)*D[y[x],x]==y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (x^5+x^4+x^3+x^2+x+1\right ) \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 31

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

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