7.13.3 problem 3

Internal problem ID [402]
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 : 3
Date solved : Saturday, March 29, 2025 at 04:52:52 PM
CAS classification : [_quadrature]

\begin{align*} 2 y^{\prime }+3 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 37

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

\[ y = \left (1-\frac {3}{2} x +\frac {9}{8} x^{2}-\frac {9}{16} x^{3}+\frac {27}{128} x^{4}-\frac {81}{1280} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 41

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

\[ y(x)\to c_1 \left (-\frac {81 x^5}{1280}+\frac {27 x^4}{128}-\frac {9 x^3}{16}+\frac {9 x^2}{8}-\frac {3 x}{2}+1\right ) \]

✓ Sympy. Time used: 0.666 (sec). Leaf size: 48

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

\[ y{\left (x \right )} = C_{1} - \frac {3 C_{1} x}{2} + \frac {9 C_{1} x^{2}}{8} - \frac {9 C_{1} x^{3}}{16} + \frac {27 C_{1} x^{4}}{128} - \frac {81 C_{1} x^{5}}{1280} + O\left (x^{6}\right ) \]