Internal problem ID [7719]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 232.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (12 x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(6*x^2*diff(y(x),x$2)+x*(1+18*x)*diff(y(x),x)+(1+12*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, {\mathrm e}^{-3 x}+c_{2} \sqrt {x}\, {\mathrm e}^{-3 x} \left (\int \frac {{\mathrm e}^{3 x}}{x^{\frac {7}{6}}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 47
DSolve[6*x^2*y''[x]+x*(1+18*x)*y'[x]+(1+12*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (\frac {\sqrt [6]{3} c_2 x^{4/3} \Gamma \left (-\frac {1}{6},-3 x\right )}{(-x)^{5/6}}+c_1 \sqrt {x}\right ) \]