2.663   ODE No. 663

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

✓ Mathematica : cpu = 0.953112 (sec), leaf count = 101

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {36 a^7 x-a^6 x^6+2 a^3 e^{c_1} x^3-e^{2 c_1}}}{3 a^3}\right \},\left \{y(x)\to \frac {\sqrt {36 a^7 x-a^6 x^6+2 a^3 e^{c_1} x^3-e^{2 c_1}}}{3 a^3}\right \}\right \}\]

✓ Maple : cpu = 0.161 (sec), leaf count = 27

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

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