Internal problem ID [11860]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{2} \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 26
DSolve[x^2*y''[x]-3*x*y'[x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]