I have the following ode: $y^{'}= \frac{k}{\sqrt{y}}$ where k is a positive value.
Applying the Forward Euler method gives the following: $v^{n}=\frac{\Delta t \ k}{\sqrt{v^{n-1}}}+v^{n-1}$
I'm struggling to show stability on this method. The definition of stability that I'm using is: The method is stable if there exists some real number $C$ such that $|V^{n}|\leq C|V^0|$
The $\frac{1}{\sqrt{v^{n-1}}}$ factor is the one giving me problems, since it makes the equation nonlinear and I can't factorize $v^{n-1}$
I'm aware of the use of fixed point and Newton methods for nonlinear equations, but I don't know if those can fix my problem.
I would appreciate any help.