14.2.19 problem 20

Internal problem ID [2507]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:56:24 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {t +y+1}{t -y+3} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 32

dsolve(diff(y(t),t)=(t+y(t)+1)/(t-y(t)+3),y(t), singsol=all)
 

\[ y = 1+\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (2+t \right )+2 c_1 \right )\right ) \left (-2-t \right ) \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 57

DSolve[D[y[t],t]==(t+y[t]+1)/(t-y[t]+3),y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(t)+t+1}{-y(t)+t+3}\right )=\log \left (\frac {t^2+y(t)^2-2 y(t)+4 t+5}{2 (t+2)^2}\right )+2 \log (t+2)+c_1,y(t)\right ] \]