Internal problem ID [7415]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 696.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 50
dsolve(2*x*diff(y(x),x$2)+5*(1-2*x)*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\frac {\erfi \left (\sqrt {5}\, \sqrt {x}\right ) \left (1+10 x \right ) \sqrt {5}\, \sqrt {\pi }}{x^{\frac {3}{2}}}-\frac {10 \,{\mathrm e}^{5 x}}{x}\right )+\frac {c_{2} \left (1+10 x \right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 40
DSolve[2*x*y''[x]+5*(1-2*x)*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 L_{-\frac {1}{2}}^{\frac {3}{2}}(5 x)+\frac {c_1 (10 x+1)}{10 \sqrt {5} x^{3/2}} \\ \end{align*}