Internal problem ID [4264]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{\prime }-\cos \relax (y )+x \tan \relax (y )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 10
dsolve(diff(x(y),y)=cos(y)-x(y)*tan(y),x(y), singsol=all)
\[ x \relax (y ) = \left (y +c_{1}\right ) \cos \relax (y ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 12
DSolve[x'[y]==Cos[y]-x[y]*Tan[y],x[y],y,IncludeSingularSolutions -> True]
\begin{align*} x(y)\to (y+c_1) \cos (y) \\ \end{align*}