Internal problem ID [8245]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 772.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 81
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)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{2 i \sqrt {x}} \sqrt {\frac {\left (1+4 x \right ) \left (2 i \sqrt {x}-1\right )}{1+2 i \sqrt {x}}}}{x}+\frac {c_{2} {\mathrm e}^{-2 i \sqrt {x}} \sqrt {\frac {\left (1+4 x \right ) \left (1+2 i \sqrt {x}\right )}{2 i \sqrt {x}-1}}}{x} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 64
DSolve[2*x^2*y''[x]+3*x*y'[x]+(2*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-2 i \sqrt {x}} \left (8 c_1 e^{4 i \sqrt {x}} \left (2 \sqrt {x}+i\right )+c_2 \left (1+2 i \sqrt {x}\right )\right )}{8 x} \]