10.9.26 problem 41

Internal problem ID [1328]
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 : 41
Date solved : Tuesday, March 04, 2025 at 12:29:13 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=t^2*diff(diff(y(t),t),t)+2*t*diff(y(t),t)+1/4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 24

ode=t^2*D[y[t],{t,2}]+2*t*D[y[t],t]+25/100*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {c_2 \log (t)+2 c_1}{2 \sqrt {t}} \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 14

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

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