64.12.4 problem 4

Internal problem ID [13508]
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 : 4
Date solved : Tuesday, January 28, 2025 at 05:50:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+y(x)=sec(x)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]+y[x]==Sec[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sec (x)}{2}+c_1 \cos (x)+\sin (x) (\tan (x)+c_2) \]