Internal problem ID [6849]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 117.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 33
dsolve(6*x^2*(1+2*x^2)*diff(y(x),x$2)+x*(1+50*x^2)*diff(y(x),x)+(1+30*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{2 x^{2}+1}+\frac {c_{2} x^{\frac {1}{3}}}{2 x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 32
DSolve[6*x^2*(1+2*x^2)*y''[x]+x*(1+50*x^2)*y'[x]+(1+30*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x} \left (6 c_2 \sqrt [6]{x}+c_1\right )}{2 x^2+1} \\ \end{align*}