73.23.11 problem 33.3 (k)

Internal problem ID [15586]
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 (k)
Date solved : Monday, March 31, 2025 at 01:41:47 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

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

\[ y = \left (1+\frac {1}{2} x^{2}-\frac {1}{3} x^{3}+\frac {3}{8} x^{4}-\frac {11}{30} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 36

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

\[ y(x)\to c_1 \left (-\frac {11 x^5}{30}+\frac {3 x^4}{8}-\frac {x^3}{3}+\frac {x^2}{2}+1\right ) \]

✓ Sympy. Time used: 0.777 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = C_{1} + \frac {C_{1} x^{2}}{2} - \frac {C_{1} x^{3}}{3} + \frac {3 C_{1} x^{4}}{8} - \frac {11 C_{1} x^{5}}{30} + O\left (x^{6}\right ) \]