Internal problem ID [1683]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {t +y}{t -y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(t),t)=(t+y(t))/(t-y(t)),y(t), singsol=all)
\[ y \relax (t ) = \tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (t )+2 c_{1}\right )\right ) t \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 36
DSolve[y'[t]==(t+y[t])/(t-y[t]),y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(t)^2}{t^2}+1\right )-\text {ArcTan}\left (\frac {y(t)}{t}\right )=-\log (t)+c_1,y(t)\right ] \]