90.1.2 problem 13

Internal problem ID [25026]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 13
Date solved : Thursday, October 02, 2025 at 11:47:30 PM
CAS classification : [_separable]

\begin{align*} t y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 7

ode:=t*diff(y(t),t) = y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 t \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=t*D[y[t],{t,1}]==y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 t\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 5

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

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