63.5.34 problem 16-b(iii)

Internal problem ID [13108]
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 : Tuesday, January 28, 2025 at 04:52:39 AM
CAS classification : [NONE]

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

✓ Solution by Maple

Time used: 0.061 (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)
 

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 59

DSolve[D[x[t],t]==- (Sin[x[t]]-x[t]*Sin[t])/(t*Cos[x[t]]+Cos[t]),x[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^t(\sin (x(t))-\sin (K[1]) x(t))dK[1]+\int _1^{x(t)}\left (\cos (t)+t \cos (K[2])-\int _1^t(\cos (K[2])-\sin (K[1]))dK[1]\right )dK[2]=c_1,x(t)\right ] \]