Internal problem ID [6911]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 179.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 73
dsolve(x^2*(1+x)*diff(y(x),x$2)+x*(1-10*x)*diff(y(x),x)-(9-10*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (715 x^{4}+572 x^{3}+234 x^{2}+52 x +5\right )}{x^{3}}+c_{2} \left (8 x^{10}+91 x^{9}+468 x^{8}+1430 x^{7}+2860 x^{6}+3861 x^{5}+3432 x^{4}+1716 x^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 50
DSolve[x^2*(1+x)*y''[x]+x*(1-10*x)*y'[x]-(9-10*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6435 c_1 (x+1)^{12} (8 x-5)-8 c_2 (13 x (x (11 x (5 x+4)+18)+4)+5)}{51480 x^3} \\ \end{align*}