30.14.8 problem 8

Internal problem ID [7657]
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 : 8
Date solved : Tuesday, September 30, 2025 at 04:55:34 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-2 x y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 45

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

\[ y = \left (-1+2 x +3 \left (x -1\right )^{2}+\frac {10 \left (x -1\right )^{3}}{3}+\frac {19 \left (x -1\right )^{4}}{6}+\frac {13 \left (x -1\right )^{5}}{5}\right ) y \left (1\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 47

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

\[ y(x)\to c_1 \left (\frac {13}{5} (x-1)^5+\frac {19}{6} (x-1)^4+\frac {10}{3} (x-1)^3+3 (x-1)^2+2 (x-1)+1\right ) \]

✓ Sympy. Time used: 0.143 (sec). Leaf size: 19

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

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