Internal problem ID [14355]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(( y(t)*ln(t/y(t)) )+( t^2/(t+y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (\ln \left (\frac {1}{\textit {\_a}}\right ) \textit {\_a} +\ln \left (\frac {1}{\textit {\_a}}\right )+1\right )}d \textit {\_a} +\ln \left (t \right )+c_{1} \right ) t \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 39
DSolve[( y[t]*Log[t/y[t]] )+( t^2/(t+y[t]))*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {1}{K[1] (K[1] \log (K[1])+\log (K[1])-1)}dK[1]=\log (t)+c_1,y(t)\right ] \]