Internal problem ID [7334]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 614.
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 }+3 y^{\prime } x^{2}-\left (6-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve(x^2*(1+x)*diff(y(x),x$2)+3*x^2*diff(y(x),x)-(6-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (4+x \right )}{x^{2}}+\frac {c_{2} \left (6 \left (4+x \right ) \left (x +1\right )^{2} \ln \left (x +1\right )+60 x^{2}+129 x +68\right )}{\left (x +1\right )^{2} x^{2}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 49
DSolve[x^2*(1+x)*y''[x]+3*x^2*y'[x]-(6-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6 c_1 (x+4)+\frac {c_2 (3 x (20 x+43)+68)}{(x+1)^2}+6 c_2 (x+4) \log (x+1)}{6 x^2} \\ \end{align*}