Internal problem ID [12409]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y}{y-x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(y(x),x)=y(x)/(y(x)-x),y(1) = 1],y(x), singsol=all)
\begin{align*} y \left (x \right ) = x -\sqrt {x^{2}-1} y \left (x \right ) = x +\sqrt {x^{2}-1} \end{align*}
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 33
DSolve[{y'[x]==y[x]/(y[x]-x),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\sqrt {x^2-1} y(x)\to \sqrt {x^2-1}+x \end{align*}