62.6.1 problem Ex 1

Internal problem ID [12819]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:24:46 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(y(x),x)+y(x)*cot(x)=sec(x),y(x), singsol=all)
 

\[ y = \csc \left (x \right ) \left (-\ln \left (\cos \left (x \right )\right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 16

DSolve[D[y[x],x]+y[x]*Cot[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \csc (x) (-\log (\cos (x))+c_1) \]