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`]]
\[ \boxed {y^{\prime }-\frac {t +y+1}{t -y+3}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 32
dsolve(diff(y(t),t)=(t+y(t)+1)/(t-y(t)+3),y(t), singsol=all)
\[ y \left (t \right ) = 1+\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (2+t \right )+2 c_{1} \right )\right ) \left (-2-t \right ) \]
✓ 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]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(t)+t+1}{-y(t)+t+3}\right )=\log \left (\frac {t^2+y(t)^2-2 y(t)+4 t+5}{2 (t+2)^2}\right )+2 \log (t+2)+c_1,y(t)\right ] \]