Internal problem ID [6781]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 49.
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 (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 46
dsolve(x^2*(1+x)*diff(y(x),x$2)+x*(1+2*x)*diff(y(x),x)-(4+6*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+\frac {c_{2} \left (12 \ln \relax (x ) x^{4}-12 \ln \left (x +1\right ) x^{4}+12 x^{3}-6 x^{2}+4 x -3\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 50
DSolve[x^2*(1+x)*y''[x]+x*(1+2*x)*y'[x]-(4+6*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^2+\frac {c_2 \left (12 x^4 (\log (x)-\log (x+1))+2 \left (6 x^2-3 x+2\right ) x-3\right )}{12 x^2} \\ \end{align*}