1.13.2 problem 2

Internal problem ID [401]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 03:58:24 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

Order:=6; 
ode:=diff(y(x),x) = 4*y(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1+4 x +8 x^{2}+\frac {32}{3} x^{3}+\frac {32}{3} x^{4}+\frac {128}{15} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.0 (sec). Leaf size: 37

ode=D[y[x],x]==4*y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {128 x^5}{15}+\frac {32 x^4}{3}+\frac {32 x^3}{3}+8 x^2+4 x+1\right ) \]

✓ Sympy. Time used: 0.139 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{1} + 4 C_{1} x + 8 C_{1} x^{2} + \frac {32 C_{1} x^{3}}{3} + \frac {32 C_{1} x^{4}}{3} + \frac {128 C_{1} x^{5}}{15} + O\left (x^{6}\right ) \]