68.18.60 problem 66

Internal problem ID [17904]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 66
Date solved : Thursday, October 02, 2025 at 02:29:28 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 x y^{\prime \prime }+11 y^{\prime }-y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 44

Order:=6; 
ode:=3*x*diff(diff(y(x),x),x)+11*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \frac {c_1 \left (1-\frac {1}{5} x +\frac {1}{20} x^{2}+\frac {1}{60} x^{3}+\frac {1}{960} x^{4}+\frac {1}{33600} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{8}/{3}}}+c_2 \left (1+\frac {1}{11} x +\frac {1}{308} x^{2}+\frac {1}{15708} x^{3}+\frac {1}{1256640} x^{4}+\frac {1}{144513600} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 85

ode=3*x*D[y[x],{x,2}]+11*D[y[x],x]-y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (\frac {x^5}{144513600}+\frac {x^4}{1256640}+\frac {x^3}{15708}+\frac {x^2}{308}+\frac {x}{11}+1\right )+\frac {c_2 \left (\frac {x^5}{33600}+\frac {x^4}{960}+\frac {x^3}{60}+\frac {x^2}{20}-\frac {x}{5}+1\right )}{x^{8/3}} \]

✓ Sympy. Time used: 0.295 (sec). Leaf size: 75

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), (x, 2)) - y(x) + 11*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (\frac {x^{5}}{144513600} + \frac {x^{4}}{1256640} + \frac {x^{3}}{15708} + \frac {x^{2}}{308} + \frac {x}{11} + 1\right ) + \frac {C_{1} \left (\frac {x^{7}}{183456000} + \frac {x^{6}}{2016000} + \frac {x^{5}}{33600} + \frac {x^{4}}{960} + \frac {x^{3}}{60} + \frac {x^{2}}{20} - \frac {x}{5} + 1\right )}{x^{\frac {8}{3}}} + O\left (x^{6}\right ) \]