49.12.3 problem 2

Internal problem ID [7676]
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
Date solved : Monday, January 27, 2025 at 03:09:41 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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)
 

\[ y = \frac {9 \left (x -\frac {1}{3}\right )^{2} c_{2} +9 c_{1}}{9 x -3} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 39

DSolve[(3*x-1)^2*D[y[x],{x,2}]+(9*x-3)*D[y[x],x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \left (-9 x^2+6 x-2\right )-3 i c_2 x (3 x-2)}{6 x-2} \]