Internal problem ID [7813]
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]]
\[ \boxed {2 y^{\prime \prime } x^{2}+3 y^{\prime } x +\left (2 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.172 (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)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{2 i \sqrt {x}} \sqrt {1+4 x}\, \sqrt {\frac {2 \sqrt {x}+i}{-2 \sqrt {x}+i}}}{x}+\frac {c_{2} {\mathrm e}^{-2 i \sqrt {x}} \sqrt {1+4 x}\, \sqrt {\frac {-2 \sqrt {x}+i}{2 \sqrt {x}+i}}}{x} \]
✓ 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]
\[ y(x)\to \frac {e^{-2 i \sqrt {x}} \left (8 c_1 e^{4 i \sqrt {x}} \left (2 \sqrt {x}+i\right )+c_2 \left (1+2 i \sqrt {x}\right )\right )}{8 x} \]