Internal problem ID [8183]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 708.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(2*x^2*diff(y(x),x$2)-(3*x+2)*diff(y(x),x)+(2*x-1)/x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (5 x +2\right )}{\sqrt {x}}+\frac {c_{2} \left (5 x +2\right ) \left (\int \frac {x^{\frac {5}{2}} {\mathrm e}^{-\frac {1}{x}}}{\left (5 x +2\right )^{2}}d x \right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 70
DSolve[2*x^2*y''[x]-(3*x+2)*y'[x]+(2*x-1)/x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 \sqrt {\pi } c_2 (5 x+2) \text {erf}\left (\frac {1}{\sqrt {x}}\right )}{3 \sqrt {x}}+\frac {2}{3} c_2 e^{-1/x} \left (x^2-4 x-2\right )+\frac {c_1 (5 x+2)}{5 \sqrt {x}} \]