Internal problem ID [6851]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 119.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 29
dsolve(8*x^2*(2-x^2)*diff(y(x),x$2)+2*x*(10-21*x^2)*diff(y(x),x)-(2+35*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}\, \left (x^{2}-2\right )}+\frac {c_{2} x^{\frac {1}{4}}}{x^{2}-2} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 34
DSolve[8*x^2*(2-x^2)*y''[x]+2*x*(10-21*x^2)*y'[x]-(2+35*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {3 c_1}{\sqrt {x}}+4 c_2 \sqrt [4]{x}}{6-3 x^2} \\ \end{align*}