4.9.29 problem 44

Internal problem ID [1331]
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 : 44
Date solved : Tuesday, September 30, 2025 at 04:32:42 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=4*t^2*diff(diff(y(t),t),t)-8*t*diff(y(t),t)+9*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

ode=4*t^2*D[y[t],{t,2}]-8*t*D[y[t],t]+9*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} t^{3/2} (3 c_2 \log (t)+2 c_1) \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*t**2*Derivative(y(t), (t, 2)) - 8*t*Derivative(y(t), t) + 9*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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