10.8.26 problem 40

Internal problem ID [1298]
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 : 40
Date solved : Saturday, March 29, 2025 at 10:51:35 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 24

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

\[ y(t)\to t (c_2 \cos (2 \log (t))+c_1 \sin (2 \log (t))) \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 20

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

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