90.22.6 problem 6

Internal problem ID [25344]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 353
Problem number : 6
Date solved : Friday, October 03, 2025 at 12:00:26 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }-21 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=t^2*diff(diff(y(t),t),t)-3*t*diff(y(t),t)-21*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_1}{t^{3}}+c_2 \,t^{7} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

ode=t^2*D[y[t],{t,2}]-3*t*D[y[t],t]-21*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_2 t^7+\frac {c_1}{t^3} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 3*t*Derivative(y(t), t) - 21*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t^{3}} + C_{2} t^{7} \]