3.4 problem 1(d)

Internal problem ID [5183]

Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x)-tan(x)*y(x)=exp(sin(x)),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.178 (sec). Leaf size: 15

DSolve[y'[x]-Tan[x]*y[x]==Exp[Sin[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sec (x) \left (e^{\sin (x)}+c_1\right ) \\ \end{align*}