30.14.7 problem 7

Internal problem ID [7656]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:55:34 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 24

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

\[ y(x)\to c_1 \left (\frac {1}{2} (x-1)^4-(x-1)^2+1\right ) \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 41

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

\[ y{\left (x \right )} = C_{1} + 2 C_{1} x + C_{1} x^{2} - \frac {2 C_{1} x^{3}}{3} - \frac {5 C_{1} x^{4}}{6} - \frac {C_{1} x^{5}}{15} + O\left (x^{6}\right ) \]