29.4.24 problem 113

Internal problem ID [4715]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 113
Date solved : Monday, January 27, 2025 at 09:33:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

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

\[ y \left (x \right ) = -\arctan \left (\sec \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 1.615 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \arctan (-\sec (x)+c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}