8.5.36 problem 36

Internal problem ID [764]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 36
Date solved : Monday, January 27, 2025 at 03:04:08 AM
CAS classification : [_exact]

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

✓ Solution by Maple

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

dsolve(1+exp(x*y(x))*y(x)+(exp(x*y(x))*x+2*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: 0.244 (sec). Leaf size: 18

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

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