Internal problem ID [7042]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 311.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 32
dsolve(x*(x+2)*diff(y(x),x$2)+2*(x+1)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x +1\right )+c_{2} \left (\frac {\left (-x -1\right ) \ln \left (x +2\right )}{2}+1+\frac {\left (x +1\right ) \ln \relax (x )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 26
DSolve[x*(x+2)*y''[x]+2*(x+1)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+1)+c_2 (x+1) \tanh ^{-1}(x+1)-c_2 \\ \end{align*}