74.2.10 problem 15

Internal problem ID [15780]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 15
Date solved : Monday, March 31, 2025 at 01:48:35 PM
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: 16

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: 0.215 (sec). Leaf size: 71

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]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(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