28.1.100 problem 123

Internal problem ID [4406]
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 : 123
Date solved : Monday, January 27, 2025 at 09:14:59 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }+\frac {y}{x}&={\mathrm e}^{y x} \end{align*}

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 21

dsolve(diff(y(x),x)+y(x)/x=exp(x*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.398 (sec). Leaf size: 23

DSolve[D[y[x],x]+y[x]/x==Exp[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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