74.7.11 problem 11

Internal problem ID [16088]
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 : Tuesday, January 28, 2025 at 08:38:49 AM
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*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

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

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

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