Internal problem ID [7999]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 523.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(2*x^2*diff(y(x),x$2)+x*(3+2*x)*diff(y(x),x)-(1-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-x}}{x}+\frac {c_{2} {\mathrm e}^{-x} \left (\int \sqrt {x}\, {\mathrm e}^{x}d x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 33
DSolve[2*x^2*y''[x]+x*(3+2*x)*y'[x]-(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (c_2 x^{3/2} L_{-\frac {3}{2}}^{\frac {3}{2}}(x)+c_1\right )}{x} \]