12.7.14 problem 14

Internal problem ID [1724]
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
Date solved : Monday, January 27, 2025 at 05:32:38 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \cos \left (x \right ) \cos \left (y\right )+\left (\sin \left (x \right ) \cos \left (y\right )-\sin \left (x \right ) \sin \left (y\right )+y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 19

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)
 

\[ \left (\sin \left (x \right ) \cos \left (y\right )+y-1\right ) {\mathrm e}^{y}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 28

DSolve[(Cos[x]*Cos[y[x]])+(Sin[x]*Cos[y[x]]-Sin[x]*Sin[y[x]]+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-2 e^{y(x)} (y(x)-1)-2 e^{y(x)} \sin (x) \cos (y(x))=c_1,y(x)\right ] \]