44.5.20 problem 20

Internal problem ID [7082]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:47:24 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

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

\[ y = 2 \operatorname {LambertW}\left (\frac {\left (x -3\right )^{{5}/{2}} {\mathrm e}^{\frac {x}{2}-\frac {1}{2}+\frac {c_{1}}{2}}}{2}\right )+1 \]

✓ Solution by Mathematica

Time used: 60.041 (sec). Leaf size: 61

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

\begin{align*} y(x)\to 1+2 W\left (-\frac {1}{2} \sqrt {(x-3)^5 e^{x-1+c_1}}\right ) \\ y(x)\to 1+2 W\left (\frac {1}{2} \sqrt {(x-3)^5 e^{x-1+c_1}}\right ) \\ \end{align*}