74.6.52 problem 59 (i)

Internal problem ID [15996]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 59 (i)
Date solved : Thursday, March 13, 2025 at 07:10:06 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\begin{align*} y &= -t \\ y &= -c_{1} -t \\ y &= -t +c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

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

\begin{align*} y(t)\to -t \\ y(t)\to -t+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 5

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

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