28.1.16 problem 16

Internal problem ID [4322]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 16
Date solved : Monday, January 27, 2025 at 09:02:31 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +y-1}{x -y-2} \end{align*}

✓ Solution by Maple

Time used: 0.397 (sec). Leaf size: 47

dsolve(diff(y(x),x)=(2*x+y(x)-1)/(x-y(x)-2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 75

DSolve[D[y[x],x]==(2*x+y[x]-1)/(x-y[x]-2),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {y(x)+2 x-1}{\sqrt {2} (-y(x)+x-2)}\right )+\log (9)=2 \log \left (\frac {2 x^2+y(x)^2+2 y(x)-4 x+3}{(x-1)^2}\right )+4 \log (x-1)+3 c_1,y(x)\right ] \]