Internal problem ID [4485]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson
10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise
10.10, page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime }=-{\mathrm e}^{x} \left (x +1\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((exp(x)*(x+1))+(y(x)*exp(y(x))-x*exp(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ x \,{\mathrm e}^{-y \left (x \right )+x}+\frac {y \left (x \right )^{2}}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.291 (sec). Leaf size: 26
DSolve[(Exp[x]*(x+1))+(y[x]*Exp[y[x]]-x*Exp[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} y(x)^2-x e^{x-y(x)}=c_1,y(x)\right ] \]