Internal problem ID [4373]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (\cos \relax (y) x -{\mathrm e}^{-\sin \relax (y)}\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.155 (sec). Leaf size: 17
dsolve((x*cos(y(x)) - exp(-sin(y(x))))*diff(y(x),x)+1=0,y(x), singsol=all)
\[ x -\left (y \relax (x )+c_{1}\right ) {\mathrm e}^{-\sin \left (y \relax (x )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.79 (sec). Leaf size: 26
DSolve[(x*Cos[y[x]] - Exp[-Sin[y[x]]])*y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=y(x) e^{-\sin (y(x))}+c_1 e^{-\sin (y(x))},y(x)\right ] \]