ODE No. 641

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

✓ Mathematica : cpu = 0.15289 (sec), leaf count = 35

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

\[\left \{\left \{y(x)\to \frac {4 x^8-24 c_1 x^5+36 c_1{}^2 x^2-9}{36 x^2}\right \}\right \}\]

✓ Maple : cpu = 0.378 (sec), leaf count = 26

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

\[c_{1} -\frac {\sqrt {4 x^{2} y \left (x \right )+1}}{x}+\frac {2 x^{3}}{3} = 0\]