Internal problem ID [4556]
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 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(x*(x+1)^2*diff(y(x),x$2)+(1-x^2)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x +1\right )+c_{2} \left (x +1\right ) \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 17
DSolve[x*(x+1)^2*y''[x]+(1-x^2)*y'[x]+(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+1) (c_2 \log (x)+c_1) \\ \end{align*}