Internal problem ID [7660]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 172.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(x^2*diff(y(x),x$2)+x*(2+x)*diff(y(x),x)-(2-3*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} x +\frac {c_{2} {\mathrm e}^{-x} \left (\operatorname {expIntegral}_{1}\left (-x \right ) x^{3}+{\mathrm e}^{x} x^{2}+x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}\right )}{6 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 46
DSolve[x^2*y''[x]+x*(2+x)*y'[x]-(2-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (c_2 \left (x^3 \operatorname {ExpIntegralEi}(x)-e^x \left (x^2+x+2\right )\right )+6 c_1 x^3\right )}{6 x^2} \]