78.3.30 problem 7.g

Internal problem ID [21026]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 4, Series solutions. Problems section 4.9
Problem number : 7.g
Date solved : Thursday, October 02, 2025 at 07:01:33 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (4+x \right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 40

Order:=6; 
ode:=x*diff(diff(y(x),x),x)-(x+4)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{5} \left (1+\frac {1}{2} x +\frac {1}{7} x^{2}+\frac {5}{168} x^{3}+\frac {5}{1008} x^{4}+\frac {1}{1440} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \left (2880+1440 x +240 x^{2}+4 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 56

ode=x*D[y[x],{x,2}]-(x+4)*D[y[x],x]+2*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {x^2}{12}+\frac {x}{2}+1\right )+c_2 \left (\frac {5 x^9}{1008}+\frac {5 x^8}{168}+\frac {x^7}{7}+\frac {x^6}{2}+x^5\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - (x + 4)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : Expected Expr or iterable but got None