ODE No. 1287

$$9(x-1)x{y}^{″}(x)+3(2x-1)y^{\prime }(x)-20y(x)=0$$ ✓ Mathematica : cpu = 0.0131003 (sec), leaf count = 83

DSolve[-20*y[x] + 3*(-1 + 2*x)*Derivative[1][y][x] + 9*(-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to c_2\sqrt[3]{1-x}\sqrt[3]{x}{Q}_1^{\frac{2}{3}}(2x-1)-\frac{c_1(2-2x{)}^{2/3}\sqrt[3]{1-x}{x}^{2/3}(6x-5)}{32^{2/3}(x-1)\mathrm{\Gamma }\left(\frac{4}{3}\right)}\}\right\}$$ ✓ Maple : cpu = 0.02 (sec), leaf count = 27

dsolve(9*x*(x-1)*diff(diff(y(x),x),x)+3*(2*x-1)*diff(y(x),x)-20*y(x)=0,y(x))
 

$$y\left(x\right)=c_1(6x-5)x^{\frac{2}{3}}+c_2(6x-1){(x-1)}^{\frac{2}{3}}$$