15.1.14 problem 14

Internal problem ID [2854]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 14
Date solved : Monday, January 27, 2025 at 06:20:03 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

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

\[ y = -\arctan \left (\sec \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 1.648 (sec). Leaf size: 31

DSolve[Sin[x]*Cos[y[x]]^2+Cos[x]^2*D[y[x],x]==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*}