36.3.15 problem 16

Internal problem ID [6336]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 16
Date solved : Monday, January 27, 2025 at 01:56:53 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

\[ \frac {y \,{\mathrm e}^{x y}+c_1 y-x}{y} = 0 \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 20

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

\[ \text {Solve}\left [e^{x y(x)}-\frac {x}{y(x)}=c_1,y(x)\right ] \]