Internal problem ID [2185]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+a^{2} y=\sec \left (a x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)+a^2*y(x)=sec(a*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (a x \right ) c_{2} +\cos \left (a x \right ) c_{1} +\frac {x \sin \left (a x \right ) a -\ln \left (\sec \left (a x \right )\right ) \cos \left (a x \right )}{a^{2}} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 39
DSolve[y''[x]+a^2*y[x]==Sec[a*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (a x) \left (\log (\cos (a x))+a^2 c_1\right )+a (x+a c_2) \sin (a x)}{a^2} \]