Internal problem ID [7676]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 188.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
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)
\[ y \left (x \right ) = c_{1} x^{2} \left (x^{2}-2\right )+c_{2} x^{2} \left (x^{2}-2\right ) \left (\int \frac {{\mathrm e}^{\frac {3 x^{2}}{2}}}{\left (x^{2}-2\right )^{2} x^{5}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.26 (sec). Leaf size: 89
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]
\[ y(x)\to \frac {1}{64} \left (27 c_2 \left (x^2-2\right ) x^2 \operatorname {ExpIntegralEi}\left (\frac {3 x^2}{2}\right )+64 c_1 x^4-2 x^2 \left (9 c_2 e^{\frac {3 x^2}{2}}+64 c_1\right )+24 c_2 e^{\frac {3 x^2}{2}}+\frac {8 c_2 e^{\frac {3 x^2}{2}}}{x^2}\right ) \]