Internal problem ID [6317]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF
VARIATION OF PARAMETERS. Page 71
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\tan \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+4*y(x)=tan(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {\cos \left (2 x \right ) \ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 40
DSolve[y''[x]+4*y[x]==Tan[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} \cos (2 x) \text {arctanh}(\sin (2 x))+c_1 \cos (2 x)+\frac {1}{4} (-1+4 c_2) \sin (2 x) \]