Internal problem ID [7140]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 416.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime } x^{2}-3 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)-3*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{3}}{3}} x +\frac {c_{2} \left (x^{6} \WhittakerM \left (\frac {1}{3}, \frac {5}{6}, \frac {x^{3}}{3}\right )+\left (5 x^{3}+10\right ) \WhittakerM \left (\frac {4}{3}, \frac {5}{6}, \frac {x^{3}}{3}\right )\right ) {\mathrm e}^{\frac {x^{3}}{6}}}{x^{4}} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 39
DSolve[y''[x]-x^2*y'[x]-3*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{\frac {x^3}{3}} \left (3 c_1 x-c_2 E_{\frac {4}{3}}\left (\frac {x^3}{3}\right )\right ) \\ \end{align*}