Internal problem ID [4983]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y^{2}+\left (2 x y+\cos \left (y\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve(y(x)^2+(2*x*y(x)+cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ x +\frac {\sin \left (y \left (x \right )\right )-c_{1}}{y \left (x \right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 22
DSolve[y[x]^2+(2*x*y[x]+Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {\sin (y(x))}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]