64.12.6 problem 6

Internal problem ID [13510]
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 : 6
Date solved : Tuesday, January 28, 2025 at 05:50:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \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)*sec(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 29

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

\[ y(x)\to \cos (x) \arctan (\tan (x))+c_1 \cos (x)+\sin (x) (-\log (\cos (x))-1+c_2) \]