Internal problem ID [7469]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 750.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((1-x)*x^2*diff(y(x),x$2)+(5*x-4)*x*diff(y(x),x)+(6-9*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{1}+c_{2} x^{2} \left (\ln \relax (x ) x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 24
DSolve[(1-x)*x^2*y''[x]+(5*x-4)*x*y'[x]+(6-9*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (c_1 x-c_2 (x \log (x)+1)) \\ \end{align*}