Internal problem ID [14374]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}=0} \]
✓ Solution by Maple
Time used: 0.39 (sec). Leaf size: 31
dsolve(diff(y(t),t)=1/( 2*y(t)*exp(-t/y(t))/t+t/y(t) ),y(t), singsol=all)
\[ y \left (t \right ) = t \,{\mathrm e}^{-\operatorname {RootOf}\left (-2 \textit {\_Z} -{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}+\textit {\_Z}}+{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}+2 \ln \left (t \right )+2 c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.259 (sec). Leaf size: 43
DSolve[y'[t]==1/( 2*y[t]*Exp[-t/y[t]]/t+t/y[t] ),y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {t e^{\frac {t}{y(t)}} \left (\frac {y(t)}{t}-1\right )}{y(t)}+2 \log \left (\frac {y(t)}{t}\right )=-2 \log (t)+c_1,y(t)\right ] \]