10.9.30 problem 45

Internal problem ID [1332]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 45
Date solved : Tuesday, March 04, 2025 at 12:29:19 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 23

ode:=t^2*diff(diff(y(t),t),t)+5*t*diff(y(t),t)+13*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_1 \sin \left (3 \ln \left (t \right )\right )+c_2 \cos \left (3 \ln \left (t \right )\right )}{t^{2}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 26

ode=t^2*D[y[t],{t,2}]+5*t*D[y[t],t]+13*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {c_2 \cos (3 \log (t))+c_1 \sin (3 \log (t))}{t^2} \]

✓ Sympy. Time used: 0.187 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 5*t*Derivative(y(t), t) + 13*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1} \sin {\left (3 \log {\left (t \right )} \right )} + C_{2} \cos {\left (3 \log {\left (t \right )} \right )}}{t^{2}} \]