50.11.1 problem 1(a)

Internal problem ID [7985]
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)
Date solved : Monday, January 27, 2025 at 03:35:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\tan \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+4*y(x)=tan(2*x),y(x), singsol=all)
 

\[ y = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {\cos \left (2 x \right ) \ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]+4*y[x]==Tan[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{4} \cos (2 x) \text {arctanh}(\sin (2 x))+c_1 \cos (2 x)+\frac {1}{4} (-1+4 c_2) \sin (2 x) \]