Internal problem ID [3952]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number: Exact Differential equations. Exercise 9.9, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 28
dsolve((x-2*x*y(x)+exp(y(x)))+(y(x)-x^2+x*exp(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ -x^{2} y \relax (x )+x \,{\mathrm e}^{y \relax (x )}+\frac {x^{2}}{2}+\frac {y \relax (x )^{2}}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.331 (sec). Leaf size: 35
DSolve[(x-2*x*y[x]+Exp[y[x]])+(y[x]-x^2+x*Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 (-y(x))+\frac {x^2}{2}+x e^{y(x)}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]