10.6.16 problem 16

Internal problem ID [1233]
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
Date solved : Monday, January 27, 2025 at 04:46:19 AM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \end{align*}

✓ Solution by Maple

Time used: 0.055 (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)
 

\[ {\mathrm e}^{2 y} \sin \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.466 (sec). Leaf size: 25

DSolve[D[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],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [e^{2 y(x)} \sin (x)+e^{-x} \cos (y(x))=c_1,y(x)\right ] \]