Internal problem ID [6881]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 149.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 34
dsolve(9*x^2*diff(y(x),x$2)-3*x*(7-2*x^2)*diff(y(x),x)+(25+2*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {5}{3}} {\mathrm e}^{-\frac {x^{2}}{3}}+c_{2} x^{\frac {5}{3}} {\mathrm e}^{-\frac {x^{2}}{3}} \expIntegral \left (1, -\frac {x^{2}}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 39
DSolve[9*x^2*y''[x]-3*x*(7-2*x^2)*y'[x]+(25+2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-\frac {x^2}{3}} x^{5/3} \left (c_2 \operatorname {Ei}\left (\frac {x^2}{3}\right )+2 c_1\right ) \\ \end{align*}