Internal problem ID [562]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 27.
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 {1+\left (-\sin \relax (y)+\frac {x}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.126 (sec). Leaf size: 23
dsolve(1+(-sin(y(x))+x/y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ x -\frac {\sin \left (y \relax (x )\right )-\cos \left (y \relax (x )\right ) y \relax (x )+c_{1}}{y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 29
DSolve[1+(-Sin[y[x]]+x/y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {\sin (y(x))-y(x) \cos (y(x))}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]