20.5.9 problem Problem 9

Internal problem ID [3692]
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 9
Date solved : Sunday, March 30, 2025 at 02:05:52 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

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

\[ y = -\frac {\arcsin \left (\cos \left (x \right )+c_1 \right )}{x} \]

✓ Mathematica. Time used: 0.586 (sec). Leaf size: 17

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

\[ y(x)\to \frac {\arcsin (-\cos (x)+c_1)}{x} \]

✗ Sympy

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

Timed Out