Internal problem ID [4481]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page
64
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\cos \relax (x ) \cos \relax (y)+2 x -\left (\sin \relax (x ) \sin \relax (y)+2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 20
dsolve((cos(x)*cos(y(x))+2*x)-(sin(x)*sin(y(x))+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \sin \relax (x ) \cos \left (y \relax (x )\right )+x^{2}-y \relax (x )^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.436 (sec). Leaf size: 25
DSolve[(Cos[x]*Cos[y[x]]+2*x)-(Sin[x]*Sin[y[x]]+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-2 x^2+2 y(x)^2-2 \sin (x) \cos (y(x))=c_1,y(x)\right ] \]