90.3.5 problem 5

Internal problem ID [25069]
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 : 5
Date solved : Thursday, October 02, 2025 at 11:48:14 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = c_1 t \,{\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.148 (sec). Leaf size: 10

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

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