67.23.4 problem 33.3 (d)

Internal problem ID [16937]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.3 (d)
Date solved : Thursday, October 02, 2025 at 01:40:30 PM
CAS classification : [_separable]

\begin{align*} \left (x -3\right ) y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

Order:=6; 
ode:=(x-3)*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {y \left (0\right ) \left (x -3\right )^{2}}{9} \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 20

ode=(x-3)*D[y[x],x]-2*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {x^2}{9}-\frac {2 x}{3}+1\right ) \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 3)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{1} - \frac {2 C_{1} x}{3} + \frac {C_{1} x^{2}}{9} + O\left (x^{6}\right ) \]