Internal problem ID [4563]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (x -1\right )^{2} y^{\prime \prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x*(x-1)^2*diff(y(x),x$2)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x -1}+\frac {c_{2} \left (2 \ln \relax (x ) x -x^{2}+1\right )}{x -1} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 31
DSolve[x*(x-1)^2*y''[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x (c_2 x+c_1)+2 c_2 x \log (x)+c_2}{x-1} \\ \end{align*}