Internal problem ID [7308]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 589.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x^{2} y^{\prime \prime }+3 x \left (1-x^{2}\right ) y^{\prime }+\left (7 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(9*x^2*diff(y(x),x$2)+3*x*(1-x^2)*diff(y(x),x)+(1+7*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}} \operatorname {hypergeom}\left (\left [-1\right ], \left [1\right ], \frac {x^{2}}{6}\right )+c_{2} x^{\frac {1}{3}} \operatorname {KummerU}\left (-1, 1, \frac {x^{2}}{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 50
DSolve[9*x^2*y''[x]+3*x*(1-x^2)*y'[x]+(1+7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{72} \sqrt [3]{x} \left (\left (x^2-6\right ) \left (c_2 \operatorname {ExpIntegralEi}\left (\frac {x^2}{6}\right )+72 c_1\right )-6 c_2 e^{\frac {x^2}{6}}\right ) \\ \end{align*}