15.3.6 problem 6

Internal problem ID [2899]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 6
Date solved : Monday, January 27, 2025 at 06:27:59 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 48

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

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