Internal problem ID [3954]
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 9.11, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 x +\cos \relax (x ) y+\left (2 y+\sin \relax (x )-\sin \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve((2*x+y(x)*cos(x))+(2*y(x)+sin(x)-sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) \sin \relax (x )+x^{2}+y \relax (x )^{2}+\cos \left (y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 22
DSolve[(2*x+y[x]*Cos[x])+(2*y[x]+Sin[x]-Sin[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2+y(x)^2+y(x) \sin (x)+\cos (y(x))=c_1,y(x)\right ] \]