1.18 problem 17

Internal problem ID [2772]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 1
Problem number: 17.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }-\sec \relax (x )+\cot \relax (x ) y=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 16

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

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

Solution by Mathematica

Time used: 0.06 (sec). Leaf size: 16

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

\begin{align*} y(x)\to \csc (x) (-\log (\cos (x))+c_1) \\ \end{align*}