Internal problem ID [114]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {1+{\mathrm e}^{y x} y+\left ({\mathrm e}^{y x} x +2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ {\mathrm e}^{x y \relax (x )}+x +y \relax (x )^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 18
DSolve[1+Exp[x*y[x]]*y[x]+(Exp[x*y[x]]*x+2*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2+e^{x y(x)}+x=c_1,y(x)\right ] \]