Internal problem ID [1685]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {t +y+1}{t -y+3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 31
dsolve(diff(y(t),t)=(t+y(t)+1)/(t-y(t)+3),y(t), singsol=all)
\[ y \relax (t ) = 1-\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (2+t \right )+2 c_{1}\right )\right ) \left (2+t \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 57
DSolve[y'[t]==(t+y[t]+1)/(t-y[t]+3),y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {y(t)+t+1}{-y(t)+t+3}\right )=\log \left (\frac {t^2+y(t)^2-2 y(t)+4 t+5}{2 (t+2)^2}\right )+2 \log (t+2)+c_1,y(t)\right ] \]