1.5 problem 2 (b)

Internal problem ID [5163]

Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section: Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number: 2 (b).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y \cos \relax (x )-\sin \relax (x ) \cos \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y \relax (x ) = \sin \relax (x )-1+c_{1} {\mathrm e}^{-\sin \relax (x )} \]

Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 18

DSolve[y'[x]+Cos[x]*y[x]==Sin[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \\ \end{align*}