Internal problem ID [8085]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 609.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
dsolve(x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-3*(3+x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{3}-\frac {c_{2} \left (-\operatorname {expIntegral}_{1}\left (x \right ) x^{6}+{\mathrm e}^{-x} x^{5}-{\mathrm e}^{-x} x^{4}+2 \,{\mathrm e}^{-x} x^{3}-6 x^{2} {\mathrm e}^{-x}+24 \,{\mathrm e}^{-x} x -120 \,{\mathrm e}^{-x}\right )}{720 x^{3}} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 60
DSolve[x^2*y''[x]+x*(1+x)*y'[x]-3*(3+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 e^{-x} \left (e^x x^6 \operatorname {ExpIntegralEi}(-x)+x^5-x^4+2 x^3-6 x^2+24 x-120\right )}{720 x^3}+c_1 x^3 \]