71.4.6 problem 6

Internal problem ID [14378]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:28:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(diff(y(x),x)=y(x)/(y(x)-x),y(x), singsol=all)
 

\begin{align*} y &= x -\sqrt {x^{2}-2 c_{1}} \\ y &= x +\sqrt {x^{2}-2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 38

DSolve[D[y[x],x]==y[x]/(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-1}{(K[1]-2) K[1]}dK[1]=-\log (x)+c_1,y(x)\right ] \]