ODE No. 1286

$$(3x-1{)}^2{y}^{″}(x)+3(3x-1)y^{\prime }(x)-9y(x)-{\log }^2(3x-1)=0$$ ✓ Mathematica : cpu = 0.0860394 (sec), leaf count = 101

DSolve[-Log[-1 + 3*x]^2 - 9*y[x] + 3*(-1 + 3*x)*Derivative[1][y][x] + (-1 + 3*x)^2*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \frac{-6x-3x{\log }^2(3x-1)+{\log }^2(3x-1)+\log (3x-1)-\log (1-3x)+1}{9(3x-1)}+\frac{c_1((1-3x{)}^2+1)}{2(1-3x)}+\frac{i{c}_2((1-3x{)}^2-1)}{2(1-3x)}\}\right\}$$ ✓ Maple : cpu = 0.018 (sec), leaf count = 32

dsolve((3*x-1)^2*diff(diff(y(x),x),x)+3*(3*x-1)*diff(y(x),x)-9*y(x)-ln(3*x-1)^2=0,y(x))
 

$$y\left(x\right)=\frac{c_1}{3x-1}+(3x-1)c_2-\frac{\ln {(3x-1)}^2}{9}-\frac{2}{9}$$