28.1.102 problem 125

Internal problem ID [4408]
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 : 125
Date solved : Monday, January 27, 2025 at 09:15:01 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 15.198 (sec). Leaf size: 20

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

\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{-1}}{x^{2}}\right ) {\mathrm e}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 6.868 (sec). Leaf size: 37

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

\begin{align*} y(x)\to -e^{-2 c_1} W\left (-\frac {e^{2 c_1}}{x^2}\right ) \\ y(x)\to 0 \\ y(x)\to \frac {1}{x^2} \\ \end{align*}