15.12.18 problem 18

Internal problem ID [3162]
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
Date solved : Monday, January 27, 2025 at 07:24:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sec \left (x \right ) \tan \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)+4*y(x)=sec(x)*tan(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]+4*y[x]==Sec[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (2 x) (-\text {arctanh}(\sin (x)))+c_1 \cos (2 x)+2 \sin (x) (-1+c_2 \cos (x)) \]