74.7.14 problem 14

Internal problem ID [16012]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 14
Date solved : Thursday, March 13, 2025 at 07:13:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} \frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=2/t+1/y(t)+t/y(t)^2*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 22

ode=( 2/t+1/y[t])+(t/y[t]^2)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {t}{-1+c_1 t^2} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 10

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

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