Internal problem ID [7430]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 711.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 33
dsolve(2*x*(1-x)*diff(y(x),x$2)+(1-11*x)*diff(y(x),x)-10*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+6 x +1\right )}{\left (x -1\right )^{4}}+\frac {c_{2} \sqrt {x}\, \left (x +1\right )}{\left (x -1\right )^{4}} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 34
DSolve[2*x*(1-x)*y''[x]+(1-11*x)*y'[x]-10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \sqrt {x} (x+1)-2 c_2 (x (x+6)+1)}{(x-1)^4} \\ \end{align*}