Internal problem ID [7057]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 328.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.641 (sec). Leaf size: 85
dsolve(2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+(2*x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {4 x +1}\, {\mathrm e}^{2 i \sqrt {x}} \sqrt {\frac {2 i \sqrt {x}-1}{1+2 i \sqrt {x}}}}{x}+\frac {c_{2} \sqrt {4 x +1}\, {\mathrm e}^{-2 i \sqrt {x}} \sqrt {\frac {1+2 i \sqrt {x}}{2 i \sqrt {x}-1}}}{x} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 63
DSolve[2*x^2*y''[x]+3*x*y'[x]+(2*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-2 i \sqrt {x}} \left (8 c_1 e^{4 i \sqrt {x}} \left (2 \sqrt {x}+i\right )+2 i c_2 \sqrt {x}+c_2\right )}{8 x} \\ \end{align*}