Internal problem ID [4476]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 29
dsolve((2*x+y(x)*cos(x*y(x)))+(x*cos(x*y(x))-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (x^{4}+\sin \left (\textit {\_Z} \right ) x^{2}+c_{1} x^{2}-\textit {\_Z}^{2}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 21
DSolve[(2*x+y[x]*Cos[x*y[x]])+(x*Cos[x*y[x]]-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2-y(x)^2+\sin (x y(x))=c_1,y(x)\right ] \]