Internal problem ID [6963]
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]]
Solve \begin {gather*} \boxed {6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.102 (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)
\[ y \relax (x ) = c_{1} \sqrt {x}\, {\mathrm e}^{-3 x}+\frac {c_{2} \left (-\frac {\left (-x \right )^{\frac {5}{6}} 3^{\frac {5}{6}}}{3}+x \,{\mathrm e}^{-3 x} \left (\Gamma \left (\frac {5}{6}\right )-\Gamma \left (\frac {5}{6}, -3 x \right )\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 36
DSolve[6*x^2*y''[x]+x*(1+18*x)*y'[x]+(1+12*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \sqrt [3]{x} \left (c_1 \sqrt [6]{x}-c_2 E_{\frac {7}{6}}(-3 x)\right ) \\ \end{align*}