ODE No. 1337

\[ y''(x)=-\frac {(a+2 b+3 x) y'(x)}{2 (a+x) (b+x)}-\frac {(a-b) y(x)}{4 (a+x)^2 (b+x)} \]

✓ Mathematica : cpu = 0.0587004 (sec), leaf count = 62

DSolve[Derivative[2][y][x] == -1/4*((a - b)*y[x])/((a + x)^2*(b + x)) - ((a + 2*b + 3*x)*Derivative[1][y][x])/(2*(a + x)*(b + x)),y[x],x]

\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {\frac {b+x}{a-b}+1}}+\frac {c_2 \sqrt {b+x}}{\sqrt {a-b} \sqrt {\frac {b+x}{a-b}+1}}\right \}\right \}\]

✓ Maple : cpu = 0.066 (sec), leaf count = 27

dsolve(diff(diff(y(x),x),x) = -1/2/(x+a)*(3*x+a+2*b)/(x+b)*diff(y(x),x)-1/4*(a-b)/(x+a)^2/(x+b)*y(x),y(x))

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