<s>[INST] How to solve the equation $x^2y-y^2 = e^ax^2+x^2$ in terms of $x$? Please help me solve the following equation in terms of $x$, I have difficulty with this:
$$x^2y-y^2 = e^ax^2+x^2$$
Edit with my solution:
Rewrite the equation
$$0 = y^2 - x^2y + (e^a+1)x^2$$
Using the quadratic formula we obtain
$$y = \frac{x^2±\sqrt{x^4-4(e^a+1)x^2}}{2}$$
and simplify we obtain
$$y = \frac{x^2}{2} \pm \frac{x\sqrt{x^2-4e^a-4}}{2}$$
 [/INST] Rewrite your equation as 
$$y^2 - (x^2)y + (e^ax^2+x^2) = y^2 -by +c$$
where $b$ and $c$ correspond to the terms in brackets. Then apply the standard technique to solve a quadratic equation.
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