Internal problem ID [8958]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1379.
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 {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
dsolve(diff(diff(y(x),x),x) = 12/(x+1)^2/(x^2+2*x+3)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+2 x +3\right )}{\left (x +1\right )^{2}}+\frac {c_{2} \left (\left (3 x^{2}+6 x +9\right ) \arctan \left (\frac {\left (x +1\right ) \sqrt {2}}{2}\right )-\sqrt {2}\, \left (x^{3}+2 x^{2}+4 x +1\right )\right )}{\left (x +1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 65
DSolve[y''[x] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \left (-3 \sqrt {2} (x (x+2)+3) \text {ArcTan}\left (\frac {x+1}{\sqrt {2}}\right )+2 x (x (x+2)+4)+2\right )+2 c_1 (x (x+2)+3)}{2 (x+1)^2} \\ \end{align*}