ODE No. 437

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

✓ Mathematica : cpu = 0.524225 (sec), leaf count = 47

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

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

✓ Maple : cpu = 0.046 (sec), leaf count = 36

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

\[y \left (x \right ) = -\frac {a}{4 x}\]