Internal problem ID [6890]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 158.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.144 (sec). Leaf size: 27
dsolve(4*x^2*(1+x)*diff(y(x),x$2)+8*x^2*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{x +1}+\frac {c_{2} \sqrt {x}\, \ln \relax (x )}{x +1} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 24
DSolve[4*x^2*(1+x)*y''[x]+8*x^2*y'[x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x} (c_2 \log (x)+c_1)}{x+1} \\ \end{align*}