Internal problem ID [7733]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(x^2*diff(y(x),x$2)-x*(x+3)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x} x^{2} \left (x +1\right )+c_{2} x^{2} \left (-\operatorname {expIntegral}_{1}\left (x \right ) x -\operatorname {expIntegral}_{1}\left (x \right )+{\mathrm e}^{-x}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 34
DSolve[x^2*y''[x]-x*(x+3)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \left (c_2 e^x (x+1) \operatorname {ExpIntegralEi}(-x)+c_1 e^x (x+1)+c_2\right ) \]