74.16.5 problem 5

Internal problem ID [16440]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 5
Date solved : Monday, March 31, 2025 at 02:53:26 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 59

Order:=6; 
ode:=diff(diff(y(x),x),x)-11*diff(y(x),x)+30*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \left (1-15 x^{2}-55 x^{3}-\frac {455}{4} x^{4}-\frac {671}{4} x^{5}\right ) y \left (0\right )+\left (x +\frac {11}{2} x^{2}+\frac {91}{6} x^{3}+\frac {671}{24} x^{4}+\frac {4651}{120} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 66

ode=D[y[x],{x,2}]-11*D[y[x],x]+30*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (-\frac {671 x^5}{4}-\frac {455 x^4}{4}-55 x^3-15 x^2+1\right )+c_2 \left (\frac {4651 x^5}{120}+\frac {671 x^4}{24}+\frac {91 x^3}{6}+\frac {11 x^2}{2}+x\right ) \]

✓ Sympy. Time used: 0.778 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(30*y(x) - 11*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} \left (- \frac {455 x^{4}}{4} - 55 x^{3} - 15 x^{2} + 1\right ) + C_{1} x \left (\frac {671 x^{3}}{24} + \frac {91 x^{2}}{6} + \frac {11 x}{2} + 1\right ) + O\left (x^{6}\right ) \]