Internal problem ID [5255]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 108
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((3*x-1)^2*diff(y(x),x$2)+(9*x-3)*diff(y(x),x)-9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x -\frac {1}{3}}+c_{2} \left (x -\frac {1}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 39
DSolve[(3*x-1)^2*y''[x]+(9*x-3)*y'[x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \left (-9 x^2+6 x-2\right )-3 i c_2 x (3 x-2)}{6 x-2} \\ \end{align*}