15.6.14 problem 14

Internal problem ID [2971]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:04:55 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve(cos(y(x))^2+(x-tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arctan \left (\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x -1}\right )+x +1\right ) \]

✓ Solution by Mathematica

Time used: 60.297 (sec). Leaf size: 21

DSolve[Cos[y[x]]^2+(x-Tan[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arctan \left (W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1\right ) \]