29.1.18 problem 17

Internal problem ID [4625]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 17
Date solved : Monday, January 27, 2025 at 09:26:41 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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