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]]
\[ \boxed {6 y^{\prime \prime } x^{2}+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
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)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, {\mathrm e}^{-3 x}+\frac {c_{2} \left (-\frac {\left (-x \right )^{\frac {5}{6}} 3^{\frac {5}{6}}}{3}+x \,{\mathrm e}^{-3 x} \left (\Gamma \left (\frac {5}{6}\right )-\Gamma \left (\frac {5}{6}, -3 x \right )\right )\right )}{\sqrt {x}} \]
✓ 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]
\[ y(x)\to e^{-3 x} \left (\frac {\sqrt [6]{3} c_2 x^{4/3} \Gamma \left (-\frac {1}{6},-3 x\right )}{(-x)^{5/6}}+c_1 \sqrt {x}\right ) \]