28.1.75 problem 78

Internal problem ID [4381]
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
Date solved : Monday, January 27, 2025 at 09:09:40 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 19

DSolve[D[y[x],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*}