Internal problem ID [4590]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \tan \relax (x )-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+y(x)*tan(x)=sin(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-\ln \left (\cos \relax (x )\right )+c_{1}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 16
DSolve[y'[x]+y[x]*Tan[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x) (-\log (\cos (x))+c_1) \\ \end{align*}