12.9.19 problem 19

Internal problem ID [1775]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:34:43 AM
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*}

Using reduction of order method given that one solution is

\begin{align*} y&=x^{2} \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,x^2],singsol=all)
 

\[ y = x^{2} \left (c_1 x +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (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]
 

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