Final answer:
To find the general solution of the given differential equation, we can start by separating the variables and then integrating both sides.
Step-by-step explanation:
To find the general solution of the differential equation y' = ${2x(y^2-4)}/{(x^2+3)}$, we can start by separating the variables. First, we can multiply both sides of the equation by ${(x^2+3)}/{(y^2-4)}$ to remove the fraction:
(${(x^2+3)}/{(y^2-4)}$)dy = 2xdx
Now, we integrate both sides with respect to their respective variables. On the left side, we use partial fractions to integrate:
∫(${(x^2+3)}/{(y^2-4)}$)dy = ∫2xdx