74.4.9 problem 9

Internal problem ID [15831]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 9
Date solved : Monday, March 31, 2025 at 01:57:23 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {y+2}{2 t +1} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(t),t) = (y(t)+2)/(2*t+1); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sqrt {2 t +1}\, c_1 -2 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 24

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

\begin{align*} y(t)\to -2+c_1 \sqrt {2 t+1} \\ y(t)\to -2 \\ \end{align*}

✓ Sympy. Time used: 0.223 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (y(t) + 2)/(2*t + 1),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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