Internal problem ID [2652]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +y-1}{x -y-2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 50
dsolve(diff(y(x),x)=(2*x+y(x)-1)/(x-y(x)-2),y(x), singsol=all)
\[ y \relax (x ) = -1-\tan \left (\RootOf \left (\sqrt {2}\, \ln \left (2 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \left (x -1\right )^{2}+2 \left (x -1\right )^{2}\right )+2 \sqrt {2}\, c_{1}+2 \textit {\_Z} \right )\right ) \left (x -1\right ) \sqrt {2} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 75
DSolve[y'[x]==(2*x+y[x]-1)/(x-y[x]-2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {2} \text {ArcTan}\left (\frac {y(x)+2 x-1}{\sqrt {2} (-y(x)+x-2)}\right )+\log (9)=2 \log \left (\frac {2 x^2+y(x)^2+2 y(x)-4 x+3}{(x-1)^2}\right )+4 \log (x-1)+3 c_1,y(x)\right ] \]