ODE No. 1260

$$y^{\prime }(x)(x(\text{a1}+\text{b1}+1)-\text{d1})+\text{a1}\text{b1}\text{d1}+(x-1)x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.221147 (sec), leaf count = 65

DSolve[a1*b1*d1 + (-d1 + (1 + a1 + b1)*x)*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \text{a1}\text{b1}x\mathrm{\Gamma }(\text{d1}+1){}_3{\tilde{F}}_2(1,\text{a1}+\text{b1}+1,1;\text{d1}+1,2;x)-\frac{c_1{x}^{1-\text{d1}}{}_2{F}_1(1-\text{d1},\text{a1}+\text{b1}-\text{d1}+1;2-\text{d1};x)}{\text{d1}-1}+c_2\}\right\}$$ ✓ Maple : cpu = 0.485 (sec), leaf count = 76

dsolve(x*(x-1)*diff(diff(y(x),x),x)+((a1+b1+1)*x-d1)*diff(y(x),x)+a1*b1*d1=0,y(x))
 

$$y\left(x\right)=\int (-\mathrm{signum}{(x-1)}^{\mathit{a}\mathit{1}+\mathit{b}\mathit{1}-\mathit{d}\mathit{1}}{(-\mathrm{signum}(x-1))}^{-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}+\mathit{d}\mathit{1}}\mathrm{hypergeom}([\mathit{d}\mathit{1},-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}+\mathit{d}\mathit{1}],[1+\mathit{d}\mathit{1}],x)\mathit{a}\mathit{1}\mathit{b}\mathit{1}+x^{-\mathit{d}\mathit{1}}{c}_1){(x-1)}^{-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}-1+\mathit{d}\mathit{1}}dx+c_2$$