85.72.1 problem 1 (a)

Internal problem ID [22937]
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. A Exercises at page 316
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 09:16:46 PM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

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

Order:=6; 
ode:=diff(y(x),x)+y(x) = 0; 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {x^5}{30}+\frac {x^4}{6}-\frac {2 x^3}{3}+2 x^2-4 x+4 \]

✓ Sympy. Time used: 0.130 (sec). Leaf size: 32

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

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