48.1.11 problem Example 3.11

Internal problem ID [7512]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.11
Date solved : Sunday, March 30, 2025 at 12:11:42 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.179 (sec). Leaf size: 22

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

\[ y = \frac {-2 c_1 \,t^{3}-1}{c_1 \,t^{3}-1} \]

✓ Mathematica. Time used: 1.482 (sec). Leaf size: 43

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

\begin{align*} y(t)\to \frac {1-2 e^{3 c_1} t^3}{1+e^{3 c_1} t^3} \\ y(t)\to -2 \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.395 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = \frac {- 2 t^{3} e^{3 C_{1}} - 1}{t^{3} e^{3 C_{1}} - 1} \]