ODE No. 1259

$$((a+1)x+b)y^{\prime }(x)-ly(x)+(x-1)x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0988282 (sec), leaf count = 120

DSolve[-(l*y[x]) + (b + (1 + a)*x)*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to (-1{)}^{b+1}{c}_2{x}^{b+1}{}_2{F}_1(\frac{a}{2}+b-\frac{1}{2}\sqrt{a^2+4l}+1,\frac{a}{2}+b+\frac{1}{2}\sqrt{a^2+4l}+1;b+2;x)+c_1{}_2{F}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2+4l},\frac{a}{2}+\frac{1}{2}\sqrt{a^2+4l};-b;x)\}\right\}$$ ✓ Maple : cpu = 0.054 (sec), leaf count = 92

dsolve(x*(x-1)*diff(diff(y(x),x),x)+((a+1)*x+b)*diff(y(x),x)-l*y(x)=0,y(x))
 

$$y\left(x\right)=c_1\mathrm{hypergeom}([\frac{a}{2}-\frac{\sqrt{a^2+4l}}{2},\frac{a}{2}+\frac{\sqrt{a^2+4l}}{2}],[-b],x)+c_2{x}^{b+1}\mathrm{hypergeom}([\frac{a}{2}-\frac{\sqrt{a^2+4l}}{2}+b+1,\frac{a}{2}+\frac{\sqrt{a^2+4l}}{2}+b+1],[b+2],x)$$