10.8.24 problem 38

Internal problem ID [1296]
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 : 38
Date solved : Tuesday, March 04, 2025 at 12:28:19 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \end{align*}

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

ode:=t^2*diff(diff(y(t),t),t)-4*t*diff(y(t),t)-6*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_1 \,t^{7}+c_2}{t} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

ode=t^2*D[y[t],{t,2}]-4*t*D[y[t],t]-6*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {c_2 t^7+c_1}{t} \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 4*t*Derivative(y(t), t) - 6*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t} + C_{2} t^{6} \]