Internal problem ID [7274]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 554.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.159 (sec). Leaf size: 35
dsolve(4*x^2*(1+3*x+x^2)*diff(y(x),x$2)-4*x*(1-3*x-3*x^2)*diff(y(x),x)+3*(1-x+x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{x^{2}+3 x +1}+\frac {c_{2} x^{\frac {3}{2}}}{x^{2}+3 x +1} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 27
DSolve[4*x^2*(1+3*x+x^2)*y''[x]-4*x*(1-3*x-3*x^2)*y'[x]+3*(1-x+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x} (c_2 x+c_1)}{x (x+3)+1} \\ \end{align*}