Internal problem ID [1074]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 14.
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 {\cos \relax (x ) \cos \relax (y)+\left (\cos \relax (y) \sin \relax (x )-\sin \relax (x ) \sin \relax (y)+y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.043 (sec). Leaf size: 22
dsolve((cos(x)*cos(y(x)))+(sin(x)*cos(y(x))-sin(x)*sin(y(x))+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \cos \left (y \relax (x )\right ) {\mathrm e}^{y \relax (x )} \sin \relax (x )+\left (y \relax (x )-1\right ) {\mathrm e}^{y \relax (x )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.246 (sec). Leaf size: 28
DSolve[(Cos[x]*Cos[y[x]])+(Sin[x]*Cos[y[x]]-Sin[x]*Sin[y[x]]+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-2 e^{y(x)} (y(x)-1)-2 e^{y(x)} \sin (x) \cos (y(x))=c_1,y(x)\right ] \]