64.13.21 problem 21

Internal problem ID [13551]
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
Date solved : Tuesday, January 28, 2025 at 05:52:41 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*}

With initial conditions

\begin{align*} y \left (2\right )&=0\\ y^{\prime }\left (2\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.014 (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)
 

\[ y = \left (x -2\right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 12

DSolve[{x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,{y[2]==0,Derivative[1][y][2]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-2) x^2 \]