Internal problem ID [9707]
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]]
\[ \boxed {y^{\prime \prime }-\frac {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(diff(diff(y(x),x),x) = 12/(x+1)^2/(x^2+2*x+3)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \left (x^{2}+2 x +3\right ) c_{2} \arctan \left (\frac {\left (x +1\right ) \sqrt {2}}{2}\right )-c_{2} \left (x^{3}+2 x^{2}+4 x +1\right ) \sqrt {2}+c_{1} \left (x^{2}+2 x +3\right )}{\left (x +1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 71
DSolve[y''[x] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-3 \sqrt {2} c_2 \left (x^2+2 x+3\right ) \arctan \left (\frac {x+1}{\sqrt {2}}\right )+2 c_1 \left (x^2+2 x+3\right )+2 c_2 \left (x^3+2 x^2+4 x+1\right )}{2 (x+1)^2} \]