Internal problem ID [6977]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 246.
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 }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)-x*(x+3)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} x^{2} \left (x +1\right )+c_{2} \left (-1+{\mathrm e}^{x} \left (x +1\right ) \expIntegral \left (1, x\right )\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 29
DSolve[x^2*y''[x]-x*(x+3)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (e^x (x+1) (c_2 \operatorname {Ei}(-x)+c_1)+c_2\right ) \\ \end{align*}