64.13.6 problem 6

Internal problem ID [13536]
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 : 6
Date solved : Tuesday, January 28, 2025 at 05:52:10 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+13*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]