1.26 problem 25

Internal problem ID [2780]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 1
Problem number: 25.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\tan \relax (x )-\left (1-y\right ) \sec \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve(diff(y(x),x)+tan(x) = (1-y(x))*sec(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x +c_{1}}{\sec \relax (x )+\tan \relax (x )} \]

Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 21

DSolve[y'[x]+Tan[x]==(1-y[x])*Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to (x+c_1) e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \\ \end{align*}