12.6.17 problem 17

Internal problem ID [1696]
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 : 17
Date solved : Saturday, March 29, 2025 at 11:33:39 PM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} 3 x^{2} \cos \left (x \right ) y-x^{3} y \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=3*x^2*cos(x)*y(x)-x^3*y(x)*sin(x)+4*x+(8*y(x)-x^4*sin(x)*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(3*x^2*Cos[x]*y[x]-x^3*y[x]*Sin[x]+4*x)+(8*y[x]-x^4*Sin[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**3*y(x)*sin(x) + 3*x**2*y(x)*cos(x) + 4*x + (-x**4*y(x)*sin(x) + 8*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out