90.3.30 problem 30

Internal problem ID [25094]
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 41
Problem number : 30
Date solved : Thursday, October 02, 2025 at 11:50:01 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \frac {c_1 \,{\mathrm e}^{t}}{\left (t +2\right )^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

ode=t*y[t]-(t+2)*D[y[t],{t,1}] ==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {c_1 e^t}{(t+2)^2}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = \frac {C_{1} e^{t}}{t^{2} + 4 t + 4} \]