32.3.7 problem Exact Differential equations. Exercise 9.10, page 79

Internal problem ID [5805]
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
Date solved : Monday, January 27, 2025 at 01:19:45 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ \frac {x^{3}}{3}+y \left (x \right )^{2} x -\frac {x^{2}}{2}-{\mathrm e}^{y \left (x \right )}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 32

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

\[ \text {Solve}\left [-\frac {x^3}{3}+\frac {x^2}{2}-x y(x)^2+e^{y(x)}=c_1,y(x)\right ] \]