2.1383   ODE No. 1383

\[ y''(x)=-\frac {y'(x) \left ((x-a)^2 (\alpha +\beta +1) (x-b)+(x-a) (-\alpha -\beta +1) (x-b)^2\right )}{(x-a)^2 (x-b)^2}-\frac {\alpha \beta (a-b)^2 y(x)}{(x-a)^2 (x-b)^2} \]

✓ Mathematica : cpu = 1.12565 (sec), leaf count = 50

DSolve[Derivative[2][y][x] == -((alpha*(a - b)^2*beta*y[x])/((-a + x)^2*(-b + x)^2)) - (((1 + alpha + beta)*(-a + x)^2*(-b + x) + (1 - alpha - beta)*(-a + x)*(-b + x)^2)*Derivative[1][y][x])/((-a + x)^2*(-b + x)^2),y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\alpha (\log (x-a)-\log (x-b))}+c_2 e^{\beta (\log (x-a)-\log (x-b))}\right \}\right \}\]

✓ Maple : cpu = 0.079 (sec), leaf count = 39

dsolve(diff(diff(y(x),x),x) = -((alpha+beta+1)*(x-a)^2*(x-b)+(1-alpha-beta)*(x-b)^2*(x-a))/(x-a)^2/(x-b)^2*diff(y(x),x)-alpha*beta*(a-b)^2/(x-a)^2/(x-b)^2*y(x),y(x))
 

\[y \left (x \right ) = c_{1} \left (\frac {a -x}{b -x}\right )^{\beta }+c_{2} \left (\frac {a -x}{b -x}\right )^{\alpha }\]