2.1260   ODE No. 1260

\[ y'(x) (x (\text {a1}+\text {b1}+1)-\text {d1})+\text {a1} \text {b1} \text {d1}+(x-1) x y''(x)=0 \]

✓ Mathematica : cpu = 0.363539 (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]
 

\[\left \{\left \{y(x)\to \text {a1} \text {b1} x \Gamma (\text {d1}+1) \, _3\tilde {F}_2(1,\text {a1}+\text {b1}+1,1;\text {d1}+1,2;x)-\frac {c_1 x^{1-\text {d1}} \, _2F_1(1-\text {d1},\text {a1}+\text {b1}-\text {d1}+1;2-\text {d1};x)}{\text {d1}-1}+c_2\right \}\right \}\]

✓ Maple : cpu = 0.713 (sec), leaf count = 80

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))
 

\[y \left (x \right ) = \int -\left (x -1\right )^{-\operatorname {a1} -\operatorname {b1} -1+\operatorname {d1}} x^{-\operatorname {d1}} \left (\operatorname {signum}\left (x -1\right )^{\operatorname {a1} +\operatorname {b1} -\operatorname {d1}} \left (-\operatorname {signum}\left (x -1\right )\right )^{-\operatorname {a1} -\operatorname {b1} +\operatorname {d1}} \operatorname {b1} \operatorname {a1} \,x^{\operatorname {d1}} \operatorname {hypergeom}\left (\left [\operatorname {d1} , -\operatorname {a1} -\operatorname {b1} +\operatorname {d1} \right ], \left [1+\operatorname {d1} \right ], x\right )-c_{1} \right )d x +c_{2}\]