28.2.59 problem 59

Internal problem ID [4502]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 59
Date solved : Monday, January 27, 2025 at 09:21:51 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: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 25

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

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