67.23.8 problem 33.3 (h)

Internal problem ID [16941]
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 (h)
Date solved : Thursday, October 02, 2025 at 01:40:32 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 5 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

Order:=6; 
ode:=(1-x)*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=5);
 

\[ y = \left (\frac {7}{2}-\frac {x}{2}+\frac {3 \left (x -5\right )^{2}}{16}-\frac {\left (x -5\right )^{3}}{16}+\frac {5 \left (x -5\right )^{4}}{256}-\frac {3 \left (x -5\right )^{5}}{512}\right ) y \left (5\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 53

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

\[ y(x)\to c_1 \left (-\frac {3}{512} (x-5)^5+\frac {5}{256} (x-5)^4-\frac {1}{16} (x-5)^3+\frac {3}{16} (x-5)^2+\frac {5-x}{2}+1\right ) \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=5,n=6)
 

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