Internal problem ID [7669]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 181.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(x^2*(1+2*x)*diff(y(x),x$2)-2*x*(3+14*x)*diff(y(x),x)+(6+100*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \left (2016 x^{4}+672 x^{3}+144 x^{2}+18 x +1\right )+c_{2} x \left (x^{9}+\frac {9}{2} x^{8}+9 x^{7}+\frac {21}{2} x^{6}+\frac {63}{8} x^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 44
DSolve[x^2*(1+2*x)*y''[x]-2*x*(3+14*x)*y'[x]+(6+100*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x (2 x+1)^9-\frac {c_2 x \left (2016 x^4+672 x^3+144 x^2+18 x+1\right )}{20160} \]