74.7.11 problem 11

Internal problem ID [16017]
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 : 11
Date solved : Monday, March 31, 2025 at 02:28:18 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

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

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{{\mathrm e}^{-2 \textit {\_a}} \cos \left (\frac {1}{\textit {\_a} +1}\right )+\textit {\_a}}d \textit {\_a} +\ln \left (t \right )+c_1 \right ) t \]

✓ Mathematica. Time used: 0.242 (sec). Leaf size: 49

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

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {e^{2 K[1]}}{\cos \left (\frac {1}{K[1]+1}\right )+e^{2 K[1]} K[1]}dK[1]=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

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

Timed Out