81.4.4 problem 5-5

Internal problem ID [21518]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-5
Date solved : Thursday, October 02, 2025 at 07:46:37 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} 1+3 x \sin \left (y\right )-x^{2} \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=1+3*x*sin(y(x))-x^2*cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {4 c_1 \,x^{4}-1}{4 x}\right ) \]

✓ Mathematica. Time used: 8.618 (sec). Leaf size: 23

ode=(1+3*x*Sin[y[x]])-x^2*Cos[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\arcsin \left (\frac {1}{4 x}+3 c_1 x^3\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*cos(y(x))*Derivative(y(x), x) + 3*x*sin(y(x)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (3*x*tan(y(x)) + 1/cos(y(x)))/x**2 cannot be solved by the factorable group method