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 : Sunday, March 30, 2025 at 10:51:42 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 17

ode:=y(x)^2+(2*x*y(x)+cos(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {\sin \left (y\right )-c_1}{y^{2}} = 0 \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 2.303 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x*y(x) + cos(y(x)))*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x y^{2}{\left (x \right )} + \sin {\left (y{\left (x \right )} \right )} = 0 \]