Internal problem ID [7401]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 682.
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 }+y^{\prime } x^{2}-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(x^2*(1+x)*diff(y(x),x$2)+x^2*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x +2\right )}{x}+\frac {c_{2} \left (4+\left (x +2\right ) \ln \left (x +1\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 30
DSolve[x^2*(1+x)*y''[x]+x^2*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 (x+2)+c_2 (x+2) \log (x+1)+4 c_2}{x} \\ \end{align*}