14.2.17 problem 18

Internal problem ID [2505]
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 : 18
Date solved : Monday, January 27, 2025 at 05:56:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 36

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

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