88.26.6 problem 6

Internal problem ID [24226]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 220
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:01:00 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 62

Order:=6; 
ode:=x*diff(diff(y(x),x),x)+2*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {c_1 \left (1+\frac {3}{2} x +\frac {3}{4} x^{2}+\frac {3}{16} x^{3}+\frac {9}{320} x^{4}+\frac {9}{3200} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) x +c_2 \left (\ln \left (x \right ) \left (3 x +\frac {9}{2} x^{2}+\frac {9}{4} x^{3}+\frac {9}{16} x^{4}+\frac {27}{320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (1-\frac {27}{4} x^{2}-\frac {21}{4} x^{3}-\frac {105}{64} x^{4}-\frac {909}{3200} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )}{x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 87

ode=x*D[y[x],{x,2}]+(2)*D[y[x],{x,1}]-3*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {9 x^4}{320}+\frac {3 x^3}{16}+\frac {3 x^2}{4}+\frac {3 x}{2}+1\right )+c_1 \left (\frac {3}{16} \left (3 x^3+12 x^2+24 x+16\right ) \log (x)-\frac {141 x^4+480 x^3+720 x^2+192 x-64}{64 x}\right ) \]

✓ Sympy. Time used: 0.198 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - 3*y(x) + 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{1} \left (\frac {9 x^{5}}{3200} + \frac {9 x^{4}}{320} + \frac {3 x^{3}}{16} + \frac {3 x^{2}}{4} + \frac {3 x}{2} + 1\right ) + O\left (x^{6}\right ) \]