85.73.2 problem 1 (b)

Internal problem ID [22955]
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 (b)
Date solved : Thursday, October 02, 2025 at 09:16:55 PM
CAS classification : [[_linear, `class A`]]

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

Using series method with expansion around

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

With initial conditions

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

Order:=6; 
ode:=diff(y(x),x)+y(x) = x^2; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = \frac {1}{3} x^{3}-\frac {1}{12} x^{4}+\frac {1}{60} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

ode=D[y[x],{x,1}]+y[x]==x^2; 
ic={y[0]==0}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to \frac {x^5}{60}-\frac {x^4}{12}+\frac {x^3}{3} \]

✓ Sympy. Time used: 0.178 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {x^{3}}{3} - \frac {x^{4}}{12} + \frac {x^{5}}{60} + O\left (x^{6}\right ) \]