64.13.29 problem 29

Internal problem ID [13559]
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 : 29
Date solved : Tuesday, January 28, 2025 at 05:52:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve((2*x-3)^2*diff(y(x),x$2)-6*(2*x-3)*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 
\[ y = \left (x -\frac {3}{2}\right ) \left (\left (x -\frac {3}{2}\right )^{2} c_{1} +c_{2} \right ) \]

Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 24

DSolve[(2*x-3)^2*D[y[x],{x,2}]-6*(2*x-3)*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to c_2 (3-2 x)^3+c_1 (3-2 x) \]