Internal problem ID [7398]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 679.
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 (x -3\right ) y^{\prime }+\left (4-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)+x*(x-3)*diff(y(x),x)+(4-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2} {\mathrm e}^{-x}+c_{2} x^{2} {\mathrm e}^{-x} \expIntegral \left (1, -x \right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 22
DSolve[x^2*y''[x]+x*(x-3)*y'[x]+(4-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} x^2 (c_2 \text {Ei}(x)+c_1) \\ \end{align*}