10.8.23 problem 37

Internal problem ID [1295]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 37
Date solved : Tuesday, March 04, 2025 at 12:28:17 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=t^2*diff(diff(y(t),t),t)+3*t*diff(y(t),t)+5/4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 30

ode=t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+125/100*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.187 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + 5*y(t)/4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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