12.6.12 problem 12

Internal problem ID [1691]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 12
Date solved : Saturday, March 29, 2025 at 11:31:53 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out