37.3.8 problem 10.4.8 (h)

Internal problem ID [6414]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second order and Homogeneous. page 318
Problem number : 10.4.8 (h)
Date solved : Monday, January 27, 2025 at 02:01:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(x*(x-1)^2*diff(y(x),x$2)-2*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {2 c_2 x \ln \left (x \right )-c_2 \,x^{2}+c_1 x +c_2}{x -1} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 33

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

\[ y(x)\to \frac {-c_2 x^2-c_1 x+2 c_2 x \log (x)+c_2}{x-1} \]