2.276   ODE No. 276

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

✓ Mathematica : cpu = 0.102072 (sec), leaf count = 61

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

\[\left \{\left \{y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+e^{2 c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+e^{2 c_1}}+e^{c_1}\right )\right \}\right \}\]

✓ Maple : cpu = 0.766 (sec), leaf count = 47

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

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