Internal problem ID [8151]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 676.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (3+x \right ) y^{\prime }+\left (-x +4\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(x^2*diff(y(x),x$2)-x*(3+x)*diff(y(x),x)+(4-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x} x^{2} \left (x^{2}+4 x +2\right )+c_{2} \left ({\mathrm e}^{x} \left (x^{2}+4 x +2\right ) \operatorname {Ei}_{1}\left (x \right )-x -3\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 52
DSolve[x^2*y''[x]-x*(3+x)*y'[x]+(4-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x^2 \left (c_2 e^x \left (x^2+4 x+2\right ) \operatorname {ExpIntegralEi}(-x)+4 c_1 e^x \left (x^2+4 x+2\right )+c_2 (x+3)\right ) \]