Internal problem ID [7289]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 569.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(x^2*(1-2*x)*diff(y(x),x$2)-x*(5-4*x)*diff(y(x),x)+(9-4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{3}}{\left (2 x -1\right )^{2}}+\frac {c_{2} x^{3} \left (2 x -\ln \relax (x )\right )}{\left (2 x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 29
DSolve[x^2*(1-2*x)*y''[x]-x*(5-4*x)*y'[x]+(9-4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3 (-2 c_2 x+c_2 \log (x)+c_1)}{(1-2 x)^2} \\ \end{align*}