50.6.2 problem 1(b)

Internal problem ID [7894]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page 32
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:31:31 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 39

dsolve((x*y(x)-1)+(x^2-x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= x -\sqrt {x^{2}-2 \ln \left (x \right )+2 c_{1}} \\ y &= x +\sqrt {x^{2}-2 \ln \left (x \right )+2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.415 (sec). Leaf size: 68

DSolve[(x*y[x]-1)+(x^2-x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+\sqrt {-\frac {1}{x}} \sqrt {-x \left (x^2-2 \log (x)+c_1\right )} \\ y(x)\to x+x \left (-\frac {1}{x}\right )^{3/2} \sqrt {-x \left (x^2-2 \log (x)+c_1\right )} \\ \end{align*}