5.34 problem 16-b(iii)

Internal problem ID [11432]

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).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [NONE]

\[ \boxed {x^{\prime }+\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}=0} \]

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 15

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

\[ \cos \left (t \right ) x \left (t \right )+t \sin \left (x \left (t \right )\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.27 (sec). Leaf size: 17

DSolve[x'[t]==- (Sin[x[t]]-x[t]*Sin[t])/(t*Cos[x[t]]+Cos[t]),x[t],t,IncludeSingularSolutions -> True]
 

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