50.11.11 problem 2(e)

Internal problem ID [7995]
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 : 2(e)
Date solved : Monday, January 27, 2025 at 03:36:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

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

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