Internal problem ID [11858]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{1} +c_{2} \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 18
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 (2 c_2 \log (x)+c_1) \]