57.5.34 problem 16-b(iii)

Internal problem ID [14389]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 16-b(iii)
Date solved : Thursday, October 02, 2025 at 09:36:10 AM
CAS classification : [NONE]

\begin{align*} x^{\prime }&=-\frac {\sin \left (x\right )-\sin \left (t \right ) x}{t \cos \left (x\right )+\cos \left (t \right )} \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 15

ode:=diff(x(t),t) = -(sin(x(t))-x(t)*sin(t))/(t*cos(x(t))+cos(t)); 
dsolve(ode,x(t), singsol=all);
 

\[ \cos \left (t \right ) x+t \sin \left (x\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 17

ode=D[x[t],t]==- (Sin[x[t]]-x[t]*Sin[t])/(t*Cos[x[t]]+Cos[t]); 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}[t \sin (x(t))+x(t) \cos (t)=c_1,x(t)] \]

✗ Sympy

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

Timed Out