Internal problem ID [7547]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 831.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (3+x \right ) y^{\prime }+\left (x +4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
dsolve(x^2*(1-2*x+x^2)*diff(y(x), x$2) -x*(3+x)*diff(y(x),x)+(4+x)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2} {\mathrm e}^{-\frac {4}{x -1}}}{x -1}+\frac {c_{2} x^{2} \expIntegral \left (1, -\frac {4 x}{x -1}\right ) {\mathrm e}^{-\frac {4 x}{x -1}}}{x -1} \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 54
DSolve[x^2*(1-2*x+x^2)*y''[x] -x*(3+x)*y'[x]+(4+x)*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {4 x}{x-1}} \sqrt {1-x} x^2 \left (c_2 \text {Ei}\left (\frac {4 x}{x-1}\right )+e^4 c_1\right )}{(x-1)^{3/2}} \\ \end{align*}