85.73.1 problem 1 (a)

Internal problem ID [22954]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 7. Solution of differential equations by use of series. B Exercises at page 316
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 09:16:55 PM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

Order:=6; 
ode:=diff(y(x),x)+3*y(x) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = 1-3 x +\frac {9}{2} x^{2}-\frac {9}{2} x^{3}+\frac {27}{8} x^{4}-\frac {81}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

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

ode=D[y[x],{x,1}]+3*y[x]==0; 
ic={y[0]==1}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to -\frac {81 x^5}{40}+\frac {27 x^4}{8}-\frac {9 x^3}{2}+\frac {9 x^2}{2}-3 x+1 \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = 1 - 3 x + \frac {9 x^{2}}{2} - \frac {9 x^{3}}{2} + \frac {27 x^{4}}{8} - \frac {81 x^{5}}{40} + O\left (x^{6}\right ) \]