64.12.2 problem 2

Internal problem ID [13506]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 05:50:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 48

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

\[ y(x)\to \cos (x) \int _1^x-\sin (K[1]) \tan ^2(K[1])dK[1]+\sin (x) \text {arctanh}(\sin (x))-\sin ^2(x)+c_1 \cos (x)+c_2 \sin (x) \]