76.15.34 problem 35

Internal problem ID [17675]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 10:53:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 29

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

\[ y(x)\to \frac {1}{3} \sin (\log (x))+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]