Internal problem ID [7324]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 604.
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 }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.101 (sec). Leaf size: 28
dsolve(4*x^2*(1+x)*diff(y(x),x$2)+4*x*(1+2*x)*diff(y(x),x)-(1+3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}+\frac {c_{2} \left (\ln \left (x +1\right ) x -\ln \relax (x ) x -1\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 32
DSolve[4*x^2*(1+x)*y''[x]+4*x*(1+2*x)*y'[x]-(1+3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x+c_2 (-x \log (x)+x \log (x+1)-1)}{\sqrt {x}} \\ \end{align*}