Internal problem ID [8089]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 613.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 74
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)
\[ y \left (x \right ) = \frac {c_{1} \left (715 x^{4}+572 x^{3}+234 x^{2}+52 x +5\right )}{x^{3}}+\frac {c_{2} \left (x^{13}+\frac {91}{8} x^{12}+\frac {117}{2} x^{11}+\frac {715}{4} x^{10}+\frac {715}{2} x^{9}+\frac {3861}{8} x^{8}+429 x^{7}+\frac {429}{2} x^{6}\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 51
DSolve[x^2*(1+x)*y''[x]+x*(1-10*x)*y'[x]-(9-10*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {6435 c_1 (x+1)^{12} (8 x-5)-8 c_2 \left (715 x^4+572 x^3+234 x^2+52 x+5\right )}{51480 x^3} \]