64.13.16 problem 16

Internal problem ID [13546]
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 : 16
Date solved : Tuesday, January 28, 2025 at 05:52:25 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 23

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

\[ y(x)\to \frac {c_1}{x^2}+2 \log (x)+\frac {c_2}{x}-3 \]