Internal problem ID [4993]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {y \,{\mathrm e}^{x y}-\frac {1}{y}+\left (x \,{\mathrm e}^{x y}+\frac {x}{y^{2}}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ \frac {y \left (x \right ) {\mathrm e}^{x y \left (x \right )}+c_{1} y \left (x \right )-x}{y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.2 (sec). Leaf size: 20
DSolve[(y[x]*Exp[x*y[x]]-1/y[x])+(x*Exp[x*y[x]]+x/y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{x y(x)}-\frac {x}{y(x)}=c_1,y(x)\right ] \]