7.5.36 problem 36

Internal problem ID [140]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 36
Date solved : Friday, February 07, 2025 at 07:57:10 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

\[ x +{\mathrm e}^{x y}+y^{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 18

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

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