9.7.9 problem problem 9

Internal problem ID [1050]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 9
Date solved : Tuesday, March 04, 2025 at 12:08:05 PM
CAS classification : [_separable]

\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 37

Order:=6; 
ode:=(x-1)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \left (6 x^5+5 x^4+4 x^3+3 x^2+2 x+1\right ) \]

✓ Sympy. Time used: 0.711 (sec). Leaf size: 39

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

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