74.4.61 problem 59

Internal problem ID [15954]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 59
Date solved : Tuesday, January 28, 2025 at 08:24:34 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

dsolve([diff(y(x),x)=-(y(x)-2)/(x-2),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {2 x}{x -2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 13

DSolve[{D[y[x],x]==-(y[x]-2)/(x-2),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x}{x-2} \]