Internal problem ID [2711]
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: 78.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-y \tan \relax (x )+y^{2} \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)-y(x)*tan(x)+y(x)^2*cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\left (x +c_{1}\right ) \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 19
DSolve[y'[x]-y[x]*Tan[x]+y[x]^2*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sec (x)}{x+c_1} \\ y(x)\to 0 \\ \end{align*}