ODE No. 1379

$$y^{″}(x)=\frac{12y(x)}{(x+1{)}^2(x^2+2x+3)}$$ ✓ Mathematica : cpu = 0.0514419 (sec), leaf count = 99

DSolve[Derivative[2][y][x] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)),y[x],x]
 

$$\left\{\{y(x)\to \frac{c_2(2x^3+4x^2-3\sqrt{2}{x}^2{\tan }^{-1}\left(\frac{x+1}{\sqrt{2}}\right)+8x-6\sqrt{2}x{\tan }^{-1}\left(\frac{x+1}{\sqrt{2}}\right)-9\sqrt{2}{\tan }^{-1}\left(\frac{x+1}{\sqrt{2}}\right)+2)}{2(x+1{)}^2}+c_1(\frac{2}{(x+1{)}^2}+1)\}\right\}$$ ✓ Maple : cpu = 0.051 (sec), leaf count = 60

dsolve(diff(diff(y(x),x),x) = 12/(1+x)^2/(x^2+2*x+3)*y(x),y(x))
 

$$y\left(x\right)=\frac{3c_2(x^2+2x+3)\arctan \left(\frac{(1+x)\sqrt{2}}{2}\right)-c_2(x^3+2x^2+4x+1)\sqrt{2}+c_1(x^2+2x+3)}{{(1+x)}^2}$$