49.1.5 problem 2 (b)

Internal problem ID [7584]
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)
Date solved : Monday, January 27, 2025 at 03:06:39 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \end{align*}

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 18

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

\[ y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \]