29.2.3 problem 28

Internal problem ID [4636]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 28
Date solved : Monday, January 27, 2025 at 09:28:55 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 12

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

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