Internal problem ID [11861]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(3*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2}+c_{2} x^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 20
DSolve[3*x^2*y''[x]-4*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^2+c_1 \sqrt [3]{x} \]