49.3.4 problem 1(d)

Internal problem ID [7604]
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)
Date solved : Monday, January 27, 2025 at 03:07:14 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\tan \left (x \right ) y&={\mathrm e}^{\sin \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \sec \left (x \right ) \left ({\mathrm e}^{\sin \left (x \right )}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 15

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

\[ y(x)\to \sec (x) \left (e^{\sin (x)}+c_1\right ) \]