50.3.25 problem 7

Internal problem ID [7849]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 7
Date solved : Monday, January 27, 2025 at 03:25:44 PM
CAS classification : [_linear]

\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(y(x),x)*sin(2*x)=2*y(x)+2*cos(x),y(x), singsol=all)
 

\[ y = \tan \left (x \right ) c_{1} -\sec \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 15

DSolve[D[y[x],x]*Sin[2*x]==2*y[x]+2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sec (x) (-1+c_1 \sin (x)) \]