72.8.31 problem 46

Internal problem ID [14724]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 46
Date solved : Monday, March 31, 2025 at 12:55:33 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = -\frac {1}{2}+t^{2} c_1 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.211 (sec). Leaf size: 10

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

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