Internal problem ID [7342]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 622.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.102 (sec). Leaf size: 29
dsolve(x^2*diff(y(x),x$2)+x*(1-3*x^2)*diff(y(x),x)-4*(1-3*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-\frac {x^{2}}{2}+1\right ) x^{2}+c_{2} \left (\frac {3 x^{2}}{2}-3\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 64
DSolve[x^2*y''[x]+x*(1-3*x^2)*y'[x]-4*(1-3*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4 \left (x^2-2\right ) \left (27 c_2 \operatorname {Ei}\left (\frac {3 x^2}{2}\right )+64 c_1\right )-2 c_2 e^{\frac {3 x^2}{2}} \left (9 x^4-12 x^2-4\right )}{64 x^2} \\ \end{align*}