29.2.4 problem 29

Internal problem ID [4637]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 29
Date solved : Monday, January 27, 2025 at 09:28:57 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 13

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

\[ y(x)\to \sin (x)+c_1 \cos (x) \]