Internal problem ID [2060]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.6, page 50
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {1-\sin \relax (x ) y-y^{\prime } \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 11
dsolve((1-y(x)*sin(x))-cos(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\tan \relax (x )+c_{1}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 13
DSolve[(1-y[x]*Sin[x])-Cos[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)+c_1 \cos (x) \\ \end{align*}