50.12.7 problem 6(a)

Internal problem ID [8011]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.4. THE USE OF A KNOWN SOLUTION TO FIND ANOTHER. Page 74
Problem number : 6(a)
Date solved : Monday, January 27, 2025 at 03:36:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)-x/(x-1)*diff(y(x),x)+1/(x-1)*y(x)=0,x],singsol=all)
 

\[ y = c_{1} x +{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 17

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

\[ y(x)\to c_1 e^x-c_2 x \]