85.73.4 problem 1 (d)

Internal problem ID [22957]
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 (d)
Date solved : Thursday, October 02, 2025 at 09:16:56 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

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

\[ y = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}-\frac {5}{48} x^{3}+\frac {1}{384} x^{4}+\frac {41}{3840} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

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

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

\[ y(x)\to c_1 \left (\frac {41 x^5}{3840}+\frac {x^4}{384}-\frac {5 x^3}{48}-\frac {x^2}{8}+\frac {x}{2}+1\right ) \]

✓ Sympy. Time used: 0.216 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} + \frac {C_{1} x}{2} - \frac {C_{1} x^{2}}{8} - \frac {5 C_{1} x^{3}}{48} + \frac {C_{1} x^{4}}{384} + \frac {41 C_{1} x^{5}}{3840} + O\left (x^{6}\right ) \]