20.5.11 problem Problem 11

Internal problem ID [3694]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 11
Date solved : Sunday, March 30, 2025 at 02:05:54 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 20

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

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

✗ Sympy

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

Timed Out