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]`]]
\[ \boxed {1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 23
dsolve(1+(-sin(y(x))+x/y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ x -\frac {-y \left (x \right ) \cos \left (y \left (x \right )\right )+\sin \left (y \left (x \right )\right )+c_{1}}{y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 29
DSolve[1+(-Sin[y[x]]+x/y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {\sin (y(x))-y(x) \cos (y(x))}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]