Internal problem ID [583]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-{\mathrm e}^{2 y} \cos \relax (x )+\cos \relax (y) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \relax (x )-\sin \relax (y) {\mathrm e}^{-x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 21
dsolve(diff(y(x),x) = (-exp(2*y(x))*cos(x)+cos(y(x))/exp(x))/(2*exp(2*y(x))*sin(x)-sin(y(x))/exp(x)),y(x), singsol=all)
\[ c_{1}+\cos \left (y \relax (x )\right ) {\mathrm e}^{-x}+{\mathrm e}^{2 y \relax (x )} \sin \relax (x ) = 0 \]
✓ Solution by Mathematica
Time used: 0.485 (sec). Leaf size: 25
DSolve[y'[x] == (-Exp[2*y[x]]*Cos[x]+Cos[y[x]]/Exp[x])/(2*Exp[2*y[x]]*Sin[x]-Sin[y[x]]/Exp[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{2 y(x)} \sin (x)+e^{-x} \cos (y(x))=c_1,y(x)\right ] \]