ODE No. 1291

\[ 48 (x-1) x y''(x)+(152 x-40) y'(x)+53 y(x)=0 \] Mathematica : cpu = 0.0596154 (sec), leaf count = 92

DSolve[53*y[x] + (-40 + 152*x)*Derivative[1][y][x] + 48*(-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {13}{12}-\frac {\sqrt {\frac {5}{2}}}{6},\frac {13}{12}+\frac {\sqrt {\frac {5}{2}}}{6};\frac {5}{6};x\right )+\sqrt [6]{-1} c_2 \sqrt [6]{x} \, _2F_1\left (\frac {5}{4}-\frac {\sqrt {\frac {5}{2}}}{6},\frac {5}{4}+\frac {\sqrt {\frac {5}{2}}}{6};\frac {7}{6};x\right )\right \}\right \}\] Maple : cpu = 0.058 (sec), leaf count = 50

dsolve(48*x*(x-1)*diff(diff(y(x),x),x)+(152*x-40)*diff(y(x),x)+53*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \hypergeom \left (\left [\frac {13}{12}-\frac {\sqrt {10}}{12}, \frac {13}{12}+\frac {\sqrt {10}}{12}\right ], \left [\frac {5}{6}\right ], x\right )+c_{2} x^{\frac {1}{6}} \hypergeom \left (\left [\frac {5}{4}-\frac {\sqrt {10}}{12}, \frac {5}{4}+\frac {\sqrt {10}}{12}\right ], \left [\frac {7}{6}\right ], x\right )\]