1.53 problem 54

Internal problem ID [2689]

Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number: 54.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {1+\cos \relax (x ) y-y^{\prime } \sin \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve((1+y(x)*cos(x))-( sin(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = \left (-\frac {1}{\tan \relax (x )}+c_{1}\right ) \sin \relax (x ) \]

Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 15

DSolve[(1+y[x]*Cos[x])-( Sin[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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