Internal problem ID [2191]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\tan \left (x \right ) \sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+4*y(x)=sec(x)*tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-2 \cos \left (x \right )^{2}+1\right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+2 c_{1} \cos \left (x \right )^{2}-c_{1} +2 \sin \left (x \right ) \cos \left (x \right ) c_{2} -2 \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Sec[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (2 x) (-\text {arctanh}(\sin (x)))+c_1 \cos (2 x)+2 \sin (x) (-1+c_2 \cos (x)) \]