Internal problem ID [3953]
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 9.10, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 26
dsolve((x^2-x+y(x)^2)-(exp(y(x))-2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {x^{3}}{3}+x y \relax (x )^{2}-\frac {x^{2}}{2}-{\mathrm e}^{y \relax (x )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 32
DSolve[(x^2-x+y[x]^2)-(Exp[y[x]]-2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {x^3}{3}+\frac {x^2}{2}-x y(x)^2+e^{y(x)}=c_1,y(x)\right ] \]