Internal problem ID [2639]
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: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (\cos ^{2}\relax (y)\right )+{\mathrm e}^{x} \tan \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 69
dsolve(x*cos(y(x))^2+exp(x)*tan(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arccos \left (\frac {\sqrt {-2 \left (c_{1} {\mathrm e}^{x}-x -1\right ) {\mathrm e}^{x}}}{2 c_{1} {\mathrm e}^{x}-2 x -2}\right ) \\ y \relax (x ) = \pi -\arccos \left (\frac {\sqrt {-2 \left (c_{1} {\mathrm e}^{x}-x -1\right ) {\mathrm e}^{x}}}{2 c_{1} {\mathrm e}^{x}-2 x -2}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.224 (sec). Leaf size: 123
DSolve[x*Cos[y[x]]^2+Exp[x]*Tan[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\sqrt {2 e^{-x} (x+1)+8 c_1}\right ) \\ y(x)\to \sec ^{-1}\left (-\sqrt {2 e^{-x} (x+1)+8 c_1}\right ) \\ y(x)\to -\sec ^{-1}\left (\sqrt {2 e^{-x} (x+1)+8 c_1}\right ) \\ y(x)\to \sec ^{-1}\left (\sqrt {2 e^{-x} (x+1)+8 c_1}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}