Internal problem ID [12322]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y}{y-x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)=y(x)/(y(x)-x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = x -\sqrt {x^{2}-2 c_{1}} y \left (x \right ) = x +\sqrt {x^{2}-2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.836 (sec). Leaf size: 80
DSolve[y'[x]==y[x]/(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\sqrt {x^2-e^{2 c_1}} y(x)\to x+\sqrt {x^2-e^{2 c_1}} y(x)\to 0 y(x)\to x-\sqrt {x^2} y(x)\to \sqrt {x^2}+x \end{align*}