Internal problem ID [11883]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (x -\frac {3}{2}\right ) \left (c_{1} +c_{2} \left (x -\frac {3}{2}\right )^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 24
DSolve[(2*x-3)^2*y''[x]-6*(2*x-3)*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 (3-2 x)^3+c_1 (3-2 x) \]