58.2.46 problem 46

Internal problem ID [9169]
Book : Second order enumerated odes
Section : section 2
Problem number : 46
Date solved : Monday, January 27, 2025 at 05:51:38 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 16

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_2 x+c_1) \]