Many Thanks!Make x the subject of y(x^2+a^2)=a^3
You want to solve $\displaystyle y(x^2+ a^2)= a^3$ for a.
Okay, multiplying the left side, $\displaystyle x^2y+ a^2y= a^3$ which is the same as $\displaystyle a^3- ya^2- x^2y= 0$. That is a cubic equation and there is a formula for the solution- unfortunately, it is very complicated.
Look at Cubic Formula -- from Wolfram MathWorld