64.13.18 problem 18

Internal problem ID [13548]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 05:52:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=4 \sin \left (\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=4*sin(ln(x)),y(x), singsol=all)
 

\[ y = \sin \left (2 \ln \left (x \right )\right ) c_{2} +\cos \left (2 \ln \left (x \right )\right ) c_{1} +\frac {4 \sin \left (\ln \left (x \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 61

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+4*y[x]==4*Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (2 \log (x)) \int _1^x\frac {2 \cos (2 \log (K[1])) \sin (\log (K[1]))}{K[1]}dK[1]+c_2 \sin (2 \log (x))+\cos (2 \log (x)) \left (-\frac {4}{3} \sin ^3(\log (x))+c_1\right ) \]