Internal problem ID [14354]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(( cos(t/(t+y(t))) )+( exp(2*y(t)/t))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a}}}{{\mathrm e}^{2 \textit {\_a}} \textit {\_a} +\cos \left (\frac {1}{\textit {\_a} +1}\right )}d \textit {\_a} +\ln \left (t \right )+c_{1} \right ) t \]
✓ Solution by Mathematica
Time used: 0.828 (sec). Leaf size: 49
DSolve[( Cos[t/(t+y[t])] )+( Exp[2*y[t]/t] )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {e^{2 K[1]}}{\cos \left (\frac {1}{K[1]+1}\right )+e^{2 K[1]} K[1]}dK[1]=-\log (t)+c_1,y(t)\right ] \]