Internal problem ID [4473]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ {\mathrm e}^{x y \relax (x )}+x^{2}-y \relax (x )^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 22
DSolve[(y[x]*Exp[x*y[x]]+2*x)+(x*Exp[x*y[x]]-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2+e^{x y(x)}-y(x)^2=c_1,y(x)\right ] \]