Internal problem ID [4462]
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]
\[ \boxed {y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) \sin \left (x \right )+x^{2}+y \left (x \right )^{2}+\cos \left (y \left (x \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.198 (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]
\[ \text {Solve}\left [x^2+y(x)^2+y(x) \sin (x)+\cos (y(x))=c_1,y(x)\right ] \]