44.3.18 problem 26

Internal problem ID [6999]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:40:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 26

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

\[ y(x)\to \cos (\log (x)) (\log (\cos (\log (x)))+c_1)+(\log (x)+c_2) \sin (\log (x)) \]