ODE No. 1281

\[ 4 x^2 y''(x)+\left (4 x^2-4 x-1\right ) y(x)-4 (2 x-1) x y'(x)=0 \]

✓ Mathematica : cpu = 0.0107898 (sec), leaf count = 28

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

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

✓ Maple : cpu = 0.049 (sec), leaf count = 15

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

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