36.3.4 problem 4

Internal problem ID [6325]
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 : 4
Date solved : Monday, January 27, 2025 at 01:56:38 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

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

\[ {\mathrm e}^{y \left (x \right ) x}+x^{2}-y \left (x \right )^{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 22

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

\[ \text {Solve}\left [x^2+e^{x y(x)}-y(x)^2=c_1,y(x)\right ] \]