74.9.13 problem 23

Internal problem ID [16118]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 23
Date solved : Monday, March 31, 2025 at 02:44:15 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

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

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

\[ y = \frac {c_2 \,t^{2}+c_1}{t} \]

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

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

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

✓ Sympy. Time used: 0.155 (sec). Leaf size: 8

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

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