Internal problem ID [11875]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 0, y^{\prime }\left (2\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(2) = 0, D(y)(2) = 4],y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (x -2\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 12
DSolve[{x^2*y''[x]-4*x*y'[x]+6*y[x]==0,{y[2]==0,y'[2]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x-2) x^2 \]