34.1.1 problem 1

Internal problem ID [6025]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 1, Nature and meaning of a differential equation between two variables. page 12
Problem number : 1
Date solved : Monday, January 27, 2025 at 01:33:33 PM
CAS classification : [_separable]

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

Solution by Maple

Time used: 0.001 (sec). Leaf size: 8

dsolve(diff(y(x),x)+y(x)*tan(x)=0,y(x), singsol=all)
 
\[ y = c_1 \cos \left (x \right ) \]

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 15

DSolve[D[y[x],x]+y[x]*Tan[x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to c_1 \cos (x) \\ y(x)\to 0 \\ \end{align*}