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*}