Internal problem ID [3200]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\left (y-2 y x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(1-(y(x)-2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-\ln \left (-1+2 x \right )+c_{1}} y \left (x \right ) = -\sqrt {-\ln \left (-1+2 x \right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 45
DSolve[1-(y[x]-2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\log (1-2 x)+2 c_1} y(x)\to \sqrt {-\log (1-2 x)+2 c_1} \end{align*}