Internal problem ID [6181]
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]
\[ \boxed {y^{\prime } \sin \left (2 x \right )-2 y=2 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)*sin(2*x)=2*y(x)+2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -\left (-\frac {1}{\sin \left (x \right )}+c_{1} \right ) \left (-\csc \left (2 x \right )+\cot \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 15
DSolve[y'[x]*Sin[2*x]==2*y[x]+2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sec (x) (-1+c_1 \sin (x)) \]