88.12.2 problem 2

Internal problem ID [24058]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:55:22 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.134 (sec). Leaf size: 36

ode:=y(x)*cos(x*y(x))+y(x)-x+(x*cos(x*y(x))+x-y(x))*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (x^{4}-2 \sin \left (\textit {\_Z} \right ) x^{2}-2 x^{2} \textit {\_Z} +2 x^{2} \sin \left (1\right )+\textit {\_Z}^{2}\right )}{x} \]

✓ Mathematica. Time used: 0.359 (sec). Leaf size: 31

ode=(y[x]*Cos[x*y[x]]+y[x]-x )+( x*Cos[x*y[x]]+x-y[x] )*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\frac {x^2}{2}+x y(x)-\frac {y(x)^2}{2}+\sin (x y(x))=\sin (1),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (x*cos(x*y(x)) + x - y(x))*Derivative(y(x), x) + y(x)*cos(x*y(x)) + y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out