For the differential equation

$y^{\text{'}}=x{y}^3$

a$)$ Show that $y=(c-x^2{)}^{-\frac{1}{2}}$ is a solution to the ODE.

b$)$ Using the solution above, find the particular solution to the IVP:

$y^{\text{'}}=x{y}^3,y(\frac{3}{5})=\frac{5}{4}$

c$)$ Why can we be sure that the solution you found in $(b)$ is unique?