Internal problem ID [8171]
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]]
\[ \boxed {2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(2*x*diff(y(x),x$2)+5*(1-2*x)*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (10 x +1\right )}{x^{\frac {3}{2}}}+\frac {c_{2} \left (10 x +1\right ) \left (\int \frac {\sqrt {x}\, {\mathrm e}^{5 x}}{\left (10 x +1\right )^{2}}d x \right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 40
DSolve[2*x*y''[x]+5*(1-2*x)*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 L_{-\frac {1}{2}}^{\frac {3}{2}}(5 x)+\frac {c_1 (10 x+1)}{10 \sqrt {5} x^{3/2}} \]