Internal problem ID [7288]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 568.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 36
dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(3-x)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2} \left (x -1\right )}{\left (x +1\right )^{3}}+\frac {c_{2} x^{2} \left (-4+\left (x -1\right ) \ln \relax (x )\right )}{\left (x +1\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 33
DSolve[x^2*(1+x)*y''[x]-x*(3-x)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 (c_1 (x-1)+c_2 (x-1) \log (x)-4 c_2)}{(x+1)^3} \\ \end{align*}