Internal problem ID [8162]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 687.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x^{2}-\left (3 x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-(3*x+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2} {\mathrm e}^{x} \left (x +4\right )+\frac {c_{2} \left (-x^{3} {\mathrm e}^{x} \left (x +4\right ) \operatorname {Ei}_{1}\left (x \right )+x^{3}+3 x^{2}-2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 59
DSolve[x^2*y''[x]-x^2*y'[x]-(3*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{24} c_2 e^x (x+4) x^2 \operatorname {ExpIntegralEi}(-x)+c_1 e^x (x+4) x^2-\frac {c_2 \left (x^3+3 x^2-2 x+2\right )}{24 x} \]