Internal problem ID [1018]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 43.
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 {-x +3 y-14}{x +y-2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.469 (sec). Leaf size: 28
dsolve(diff(y(x),x)=(-x+3*y(x)-14)/(x+y(x)-2),y(x), singsol=all)
\[ y \relax (x ) = 4+\frac {\left (2+x \right ) \left (\LambertW \left (-2 c_{1} \left (2+x \right )\right )+2\right )}{\LambertW \left (-2 c_{1} \left (2+x \right )\right )} \]
✓ Solution by Mathematica
Time used: 1.015 (sec). Leaf size: 144
DSolve[y'[x]==(-x+3*y[x]-14)/(x+y[x]-2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {2^{2/3} \left (x \log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )-(x+6) \log \left (\frac {x+2}{y(x)+x-2}\right )+6 \log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )+y(x) \left (\log \left (\frac {x+2}{y(x)+x-2}\right )-\log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )+1+\log (2)\right )+x-x \log (6)+x \log (3)-2-\log (64)\right )}{9 (-y(x)+x+6)}=\frac {1}{9} 2^{2/3} \log (x+2)+c_1,y(x)\right ] \]