Internal problem ID [6901]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 169.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.08 (sec). Leaf size: 36
dsolve(x^2*(1-2*x^2)*diff(y(x),x$2)+x*(7-13*x^2)*diff(y(x),x)-14*x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (2 x^{2}-1\right )^{\frac {5}{4}}}{x^{6}}+\frac {c_{2} \left (5 x^{4}-20 x^{2}+8\right )}{x^{6}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 43
DSolve[x^2*(1-2*x^2)*y''[x]+x*(7-13*x^2)*y'[x]-14*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {15 c_1 \left (1-2 x^2\right )^{5/4}+c_2 \left (-5 x^4+20 x^2-8\right )}{15 x^6} \\ \end{align*}