Internal problem ID [7793]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 306.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} x^{3}+c_{2} x^{2} \left (x \ln \left (x \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (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]
\[ y(x)\to x^2 (c_1 x-c_2 (x \log (x)+1)) \]