73.9.13 problem 14.2 (c)

Internal problem ID [15274]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (c)
Date solved : Tuesday, January 28, 2025 at 07:51:26 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x^{3} \end{align*}

✓ Solution by Maple

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

dsolve([x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+12*y(x)=0,x^3],singsol=all)
 

\[ y = x^{3} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 (c_2 x+c_1) \]