Answer to Question #138006 in Differential Equations for Carmela coroza

Question

Using elimination of arbitrary constant
y^2 (a-x) = x^2 (a+x)

Answer 1

Solution:

$$y^2 (a-x) = x^2 (a+x)$$

Now, take derivative w.r.t x on both side we get,

$$2yy'(a-x)-y^2=2ax+3x^2\\ \implies a = \frac{2yxy'-3x^2-y^2}{2yy'+2x}$$

Now, substitute a in original equation we get,

$$y^2(-5x^2-y^2)=x^2(4yxy'-x^2-y^2)\\$$