ODE No. 1062

\[ \frac {\left (x+\sqrt {x}-8\right ) y(x)}{4 x^2}+y''(x)-\frac {y'(x)}{\sqrt {x}}=0 \]

✓ Mathematica : cpu = 0.0150635 (sec), leaf count = 35

DSolve[((-8 + Sqrt[x] + x)*y[x])/(4*x^2) - Derivative[1][y][x]/Sqrt[x] + Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {1}{3} c_2 e^{\sqrt {x}} x^2+\frac {c_1 e^{\sqrt {x}}}{x}\right \}\right \}\]

✓ Maple : cpu = 0.031 (sec), leaf count = 19

dsolve(diff(diff(y(x),x),x)-diff(y(x),x)/x^(1/2)+1/4*(x+x^(1/2)-8)*y(x)/x^2=0,y(x))

\[y \left (x \right ) = \frac {{\mathrm e}^{\sqrt {x}} \left (c_{2} x^{3}+c_{1} \right )}{x}\]