36.3.6 problem 6

Internal problem ID [6327]
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
Date solved : Monday, January 27, 2025 at 01:56:39 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (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: 0.176 (sec). Leaf size: 22

DSolve[y[x]^2+(2*x*y[x]+Cos[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=-\frac {\sin (y(x))}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]