35.8.18 problem 18

Internal problem ID [6225]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:48:45 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 20

dsolve((x*cos(y(x)) - exp(-sin(y(x))))*diff(y(x),x)+1=0,y(x), singsol=all)
 

\[ \left (-y-c_{1} \right ) {\mathrm e}^{-\sin \left (y\right )}+x = 0 \]

✓ Solution by Mathematica

Time used: 0.746 (sec). Leaf size: 26

DSolve[(x*Cos[y[x]] - Exp[-Sin[y[x]]])*D[y[x],x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=y(x) e^{-\sin (y(x))}+c_1 e^{-\sin (y(x))},y(x)\right ] \]