68.17.7 problem 7

Internal problem ID [17825]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number : 7
Date solved : Thursday, October 02, 2025 at 02:28:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 44

Order:=6; 
ode:=9*x*diff(diff(y(x),x),x)+14*diff(y(x),x)+(x-1)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {c_1 \left (1+\frac {1}{4} x -\frac {3}{104} x^{2}-\frac {29}{6864} x^{3}+\frac {13}{65472} x^{4}+\frac {251}{11348480} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{5}/{9}}}+c_2 \left (1+\frac {1}{14} x -\frac {13}{644} x^{2}-\frac {59}{61824} x^{3}+\frac {29}{247296} x^{4}+\frac {53}{12364800} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 85

ode=9*x*D[y[x],{x,2}]+14*D[y[x],x]+(x-1)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {53 x^5}{12364800}+\frac {29 x^4}{247296}-\frac {59 x^3}{61824}-\frac {13 x^2}{644}+\frac {x}{14}+1\right )+\frac {c_2 \left (\frac {251 x^5}{11348480}+\frac {13 x^4}{65472}-\frac {29 x^3}{6864}-\frac {3 x^2}{104}+\frac {x}{4}+1\right )}{x^{5/9}} \]

✓ Sympy. Time used: 0.346 (sec). Leaf size: 78

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x*Derivative(y(x), (x, 2)) + (x - 1)*y(x) + 14*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (\frac {53 x^{5}}{12364800} + \frac {29 x^{4}}{247296} - \frac {59 x^{3}}{61824} - \frac {13 x^{2}}{644} + \frac {x}{14} + 1\right ) + \frac {C_{1} \left (\frac {251 x^{5}}{11348480} + \frac {13 x^{4}}{65472} - \frac {29 x^{3}}{6864} - \frac {3 x^{2}}{104} + \frac {x}{4} + 1\right )}{x^{\frac {5}{9}}} + O\left (x^{6}\right ) \]