88.26.9 problem 9

Internal problem ID [24229]
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 : 9
Date solved : Thursday, October 02, 2025 at 10:01:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 64

Order:=6; 
ode:=9*x^2*diff(diff(y(x),x),x)+(x^2-15*x)*diff(y(x),x)+7*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = x^{{1}/{3}} \left (x^{2} \left (1-\frac {7}{81} x +\frac {35}{8748} x^{2}-\frac {91}{708588} x^{3}+\frac {91}{28697814} x^{4}-\frac {247}{3874204890} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_1 +c_2 \left (\ln \left (x \right ) \left (\frac {4}{729} x^{2}-\frac {28}{59049} x^{3}+\frac {35}{1594323} x^{4}-\frac {91}{129140163} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (-2-\frac {2}{27} x +\frac {5}{243} x^{2}-\frac {239}{177147} x^{3}+\frac {503}{9565938} x^{4}-\frac {5713}{3874204890} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 103

ode=9*x^2*D[y[x],{x,2}]+(x^2-15*x)*D[y[x],{x,1}]+(7)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (\frac {91 x^{19/3}}{28697814}-\frac {91 x^{16/3}}{708588}+\frac {35 x^{13/3}}{8748}-\frac {7 x^{10/3}}{81}+x^{7/3}\right )+c_1 \left (-\frac {\left (35 x^2-756 x+8748\right ) x^{7/3} \log (x)}{3188646}-\frac {\left (199 x^4-5319 x^3+85293 x^2-354294 x-9565938\right ) \sqrt [3]{x}}{9565938}\right ) \]

✓ Sympy. Time used: 0.278 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*Derivative(y(x), (x, 2)) + (x**2 - 15*x)*Derivative(y(x), x) + 7*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{1} x^{\frac {7}{3}} \left (\frac {35 x^{2}}{8748} - \frac {7 x}{81} + 1\right ) + O\left (x^{6}\right ) \]