29.1.25 problem 24

Internal problem ID [4632]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 24
Date solved : Monday, January 27, 2025 at 09:28:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

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

\begin{align*} y(x)\to c_1 e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \\ y(x)\to 0 \\ \end{align*}