85.72.2 problem 1 (b)

Internal problem ID [22938]
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 (b)
Date solved : Thursday, October 02, 2025 at 09:16:46 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

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

Order:=6; 
ode:=diff(y(x),x) = x*y(x); 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(x),type='series',x=0);
 

\[ y = 5+\frac {5}{2} x^{2}+\frac {5}{8} x^{4}+\operatorname {O}\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 19

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

\[ y(x)\to \frac {5 x^4}{8}+\frac {5 x^2}{2}+5 \]

✓ Sympy. Time used: 0.157 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=6)
 

\[ y{\left (x \right )} = 5 + \frac {5 x^{2}}{2} + \frac {5 x^{4}}{8} + O\left (x^{6}\right ) \]