Internal problem ID [7098]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 369.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+2/x*diff(y(x),x)-2/(1+x)^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x \left (x +1\right )}+\frac {c_{2} \left (x^{2}+3 x +3\right )}{x +1} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 33
DSolve[y''[x]+2/x*y'[x]-2/(1+x)^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x (x (x+3)+3)+3 c_1}{3 x (x+1)} \\ \end{align*}