Internal problem ID [2782]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x )-y \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 20
dsolve(diff(y(x),x) = cos(x)+y(x)*tan(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x}{2}+\frac {\sin \left (2 x \right )}{4}+c_{1}}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 21
DSolve[y'[x]==Cos[x]+y[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \\ \end{align*}