Internal problem ID [6844]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 112.
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 (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.205 (sec). Leaf size: 35
dsolve(6*x^2*diff(y(x),x$2)+x*(1+6*x^2)*diff(y(x),x)+(1+9*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \WhittakerM \left (\frac {11}{24}, \frac {1}{24}, \frac {x^{2}}{2}\right ) {\mathrm e}^{-\frac {x^{2}}{4}}}{x^{\frac {7}{12}}}+c_{2} x^{\frac {1}{3}} {\mathrm e}^{-\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 47
DSolve[6*x^2*y''[x]+x*(1+6*x^2)*y'[x]+(1+9*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{-\frac {x^2}{2}} \sqrt [3]{x} \left (c_2 \sqrt [6]{x} E_{\frac {11}{12}}\left (-\frac {x^2}{2}\right )-2 c_1\right ) \\ \end{align*}