76.4.10 problem 10

Internal problem ID [17404]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 10:05:46 AM
CAS classification : [_linear]

\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve((y(x)/x+6*x)+(ln(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-3 x^{2}+c_{1}}{-2+\ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 20

DSolve[(y[x]/x+6*x)+(Log[x]-2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-3 x^2+c_1}{\log (x)-2} \]