15.12.11 problem 11

Internal problem ID [3155]
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 : 11
Date solved : Monday, January 27, 2025 at 07:24:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 23

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

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