Internal problem ID [7043]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 313.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*(x+2)*diff(y(x),x$2)+(x+1)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2 x^{2}+4 x +1\right )+c_{2} \left (x +1\right ) \sqrt {x \left (x +2\right )} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 53
DSolve[x*(x+2)*y''[x]+(x+1)*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (4 \log \left (\sqrt {x+2}-\sqrt {x}\right )\right )-i c_2 \sinh \left (4 \log \left (\sqrt {x+2}-\sqrt {x}\right )\right ) \\ \end{align*}