12.5.44 problem 43

Internal problem ID [1668]
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
Date solved : Monday, January 27, 2025 at 05:23:56 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 30

dsolve(diff(y(x),x)=(-x+3*y(x)-14)/(x+y(x)-2),y(x), singsol=all)
 

\[ y = \frac {\left (x +6\right ) \operatorname {LambertW}\left (-2 c_1 \left (x +2\right )\right )+2 x +4}{\operatorname {LambertW}\left (-2 c_1 \left (x +2\right )\right )} \]

✓ Solution by Mathematica

Time used: 1.016 (sec). Leaf size: 144

DSolve[D[y[x],x]==(-x+3*y[x]-14)/(x+y[x]-2),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {2^{2/3} \left (x \log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )-(x+6) \log \left (\frac {x+2}{y(x)+x-2}\right )+6 \log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )+y(x) \left (\log \left (\frac {x+2}{y(x)+x-2}\right )-\log \left (\frac {y(x)-x-6}{y(x)+x-2}\right )+1+\log (2)\right )+x-x \log (6)+x \log (3)-2-\log (64)\right )}{9 (-y(x)+x+6)}=\frac {1}{9} 2^{2/3} \log (x+2)+c_1,y(x)\right ] \]