ODE No. 163

\[ 2 a^2 x+2 x^2 y'(x)-2 y(x)^2-x y(x)=0 \]

✓ Mathematica : cpu = 0.0859333 (sec), leaf count = 43

DSolve[2*a^2*x - x*y[x] - 2*y[x]^2 + 2*x^2*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -\sqrt {-a^2} \sqrt {x} \tan \left (\frac {2 \sqrt {-a^2}}{\sqrt {x}}-c_1\right )\right \}\right \}\]

✓ Maple : cpu = 0.092 (sec), leaf count = 27

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

\[y \left (x \right ) = -i \tan \left (\frac {2 i a -\sqrt {x}\, c_{1}}{\sqrt {x}}\right ) \sqrt {x}\, a\]