46.1.1 problem 6

Internal problem ID [7291]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page 174
Problem number : 6
Date solved : Sunday, March 30, 2025 at 11:53:33 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 10

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

\[ y = y \left (0\right ) \left (1+x \right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 9

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

\[ y(x)\to c_1 (x+1) \]

✓ Sympy. Time used: 0.715 (sec). Leaf size: 10

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

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