Internal problem ID [6907]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 175.
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 +1\right ) y^{\prime }-3 \left (3+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
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)
\[ y \relax (x ) = x^{3} c_{1}+\frac {c_{2} \left (\expIntegral \left (1, x\right ) x^{6}-{\mathrm e}^{-x} \left (x^{5}-x^{4}+2 x^{3}-6 x^{2}+24 x -120\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 56
DSolve[x^2*y''[x]+x*(1+x)*y'[x]-3*(3+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 e^{-x} \left (e^x x^6 \text {Ei}(-x)+(x (x ((x-1) x+2)-6)+24) x-120\right )}{720 x^3}+c_1 x^3 \\ \end{align*}