Internal problem ID [3151]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x*cos(y(x))^2+tan(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \operatorname {arccot}\left (\frac {1}{\sqrt {-x^{2}-2 c_{1}}}\right ) y \left (x \right ) = \pi -\operatorname {arccot}\left (\frac {1}{\sqrt {-x^{2}-2 c_{1}}}\right ) \end{align*}
✓ Solution by Mathematica
Time used: 1.202 (sec). Leaf size: 103
DSolve[x*Cos[y[x]]^2+Tan[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\sqrt {-x^2+8 c_1}\right ) y(x)\to \sec ^{-1}\left (-\sqrt {-x^2+8 c_1}\right ) y(x)\to -\sec ^{-1}\left (\sqrt {-x^2+8 c_1}\right ) y(x)\to \sec ^{-1}\left (\sqrt {-x^2+8 c_1}\right ) y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}