ODE No. 1332

\[ y''(x)=\frac {y'(x)}{x+1}-\frac {(3 x+1) y(x)}{4 x^2 (x+1)} \]

✓ Mathematica : cpu = 0.0160325 (sec), leaf count = 26

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

\[\left \{\left \{y(x)\to c_1 \sqrt {x}+c_2 \sqrt {x} (x+\log (x))\right \}\right \}\]

✓ Maple : cpu = 0.031 (sec), leaf count = 17

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

\[y \left (x \right ) = \sqrt {x}\, \left (c_{2} \ln \left (x \right )+c_{2} x +c_{1} \right )\]