Internal problem ID [7280]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 560.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 33
dsolve(x^2*diff(y(x),x$2)-x*(5-x)*diff(y(x),x)+(9-4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{3} \left (x +1\right )+c_{2} x^{3} \left (\expIntegral \left (1, x\right ) x +\expIntegral \left (1, x\right )-{\mathrm e}^{-x}\right ) \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 34
DSolve[x^2*y''[x]-x*(5-x)*y'[x]+(9-4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} x^3 \left (e^x (x+1) (c_2 \operatorname {Ei}(-x)+c_1)+c_2\right ) \\ \end{align*}