3.7.7 problem problem 7

Internal problem ID [1048]
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 7
Date solved : Tuesday, September 30, 2025 at 04:21:11 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

\[ y = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

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

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

\[ y(x)\to c_1 \left (32 x^5+16 x^4+8 x^3+4 x^2+2 x+1\right ) \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*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)
 

\[ y{\left (x \right )} = C_{1} + 2 C_{1} x + 4 C_{1} x^{2} + 8 C_{1} x^{3} + 16 C_{1} x^{4} + 32 C_{1} x^{5} + O\left (x^{6}\right ) \]