3.25 problem 7

Internal problem ID [5428]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime } \sin \left (2 x \right )-2 y-2 \cos \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 25

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

\[ y \relax (x ) = -\left (-\frac {1}{\sin \relax (x )}+c_{1}\right ) \left (-\csc \left (2 x \right )+\cot \left (2 x \right )\right ) \]

Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 15

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

\begin{align*} y(x)\to \sec (x) (-1+c_1 \sin (x)) \\ \end{align*}