30.3.11 problem 12

Internal problem ID [7467]
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
Date solved : Tuesday, September 30, 2025 at 04:36:33 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 90

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

\[ \text {Solve}\left [\int _1^x(-\cos (K[1]-y(x))-\cos (K[1]+y(x))-4 K[1])dK[1]+\int _1^{y(x)}\left (\cos (x-K[2])-\cos (x+K[2])+4 K[2]-\int _1^x(\sin (K[1]+K[2])-\sin (K[1]-K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out