15.12.12 problem 12

Internal problem ID [3156]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:24:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 40

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

\[ y = \sin \left (a x \right ) c_2 +\cos \left (a x \right ) c_{1} +\frac {x \sin \left (a x \right ) a -\ln \left (\sec \left (a x \right )\right ) \cos \left (a x \right )}{a^{2}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 39

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

\[ y(x)\to \frac {\cos (a x) \left (\log (\cos (a x))+a^2 c_1\right )+a (x+a c_2) \sin (a x)}{a^2} \]