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`]]
\[ \boxed {y^{\prime }-\frac {t +y}{t -y}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve(diff(y(t),t)=(t+y(t))/(t-y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (t \right )+2 c_{1} \right )\right ) t \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 36
DSolve[y'[t]==(t+y[t])/(t-y[t]),y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(t)^2}{t^2}+1\right )-\arctan \left (\frac {y(t)}{t}\right )=-\log (t)+c_1,y(t)\right ] \]