71.8.31 problem 11 (b)

Internal problem ID [14465]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 11 (b)
Date solved : Tuesday, January 28, 2025 at 06:39:22 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 27

dsolve([diff(y(x),x)=y(x)/(y(x)-x),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 35

DSolve[{D[y[x],x]==y[x]/(y[x]-x),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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