28.1.55 problem 56

Internal problem ID [4361]
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
Date solved : Monday, January 27, 2025 at 09:09:10 AM
CAS classification : [_separable]

\begin{align*} 1-\left (y-2 y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (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 (2 x -1\right )+c_{1}} \\ y \left (x \right ) &= -\sqrt {-\ln \left (2 x -1\right )+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 45

DSolve[1-(y[x]-2*x*y[x])*D[y[x],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*}