Internal problem ID [7275]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 555.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.117 (sec). Leaf size: 23
dsolve(3*x^2*(1+x)^2*diff(y(x),x$2)-x*(1-10*x-11*x^2)*diff(y(x),x)+(1+5*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\left (x +1\right )^{2}}+\frac {c_{2} x^{\frac {1}{3}}}{\left (x +1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 29
DSolve[3*x^2*(1+x)^2*y''[x]-x*(1-10*x-11*x^2)*y'[x]+(1+5*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 \sqrt [3]{x}+3 c_2 x}{2 (x+1)^2} \\ \end{align*}