29.2.2 problem 27

Internal problem ID [4635]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 27
Date solved : Monday, January 27, 2025 at 09:28:53 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

\[ y \left (x \right ) = \frac {\left (x +2 c_{1} \right ) \sec \left (x \right )}{2}+\frac {\sin \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \]