10.8.27 problem 41

Internal problem ID [1299]
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 : 41
Date solved : Saturday, March 29, 2025 at 10:51:37 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_2 \,t^{4}+c_1}{t^{3}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.152 (sec). Leaf size: 10

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

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