29.1.26 problem 25

Internal problem ID [4633]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 25
Date solved : Monday, January 27, 2025 at 09:28:49 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.587 (sec). Leaf size: 21

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

\[ y(x)\to (x+c_1) e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \]