Internal problem ID [7735]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 248.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(x^2*diff(y(x),x$2)-x^2*diff(y(x),x)-(3*x+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2} {\mathrm e}^{x} \left (x +4\right )-\frac {c_{2} \left (-\operatorname {expIntegral}_{1}\left (x \right ) x^{4}+{\mathrm e}^{-x} x^{3}-4 \,\operatorname {expIntegral}_{1}\left (x \right ) x^{3}+3 x^{2} {\mathrm e}^{-x}-2 \,{\mathrm e}^{-x} x +2 \,{\mathrm e}^{-x}\right ) {\mathrm e}^{x}}{24 x} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 59
DSolve[x^2*y''[x]-x^2*y'[x]-(3*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{24} c_2 e^x (x+4) x^2 \operatorname {ExpIntegralEi}(-x)+c_1 e^x (x+4) x^2-\frac {c_2 \left (x^3+3 x^2-2 x+2\right )}{24 x} \]