Internal problem ID [5377]
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 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 3(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-2 \sin \relax (x ) \cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 12
dsolve([diff(y(x),x)=2*sin(x)*cos(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {3}{2}-\frac {\cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 17
DSolve[{y'[x]==2*Sin[x]*Cos[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (3-\cos (2 x)) \\ \end{align*}