So, we have:
In this case, f(x) = 6x^2 and g(y) = y^2.
The given differential equation is a separable differential equation, which means that it can be written in the form: solve the differential equation. dy dx 6x2y2
C = -1
The integral of 1/y^2 with respect to y is -1/y, and the integral of 6x^2 with respect to x is 2x^3 + C, where C is the constant of integration. So, we have: In this case, f(x) = 6x^2 and g(y) = y^2
A differential equation is an equation that relates a function to its derivatives. In this case, we have a first-order differential equation, which involves a first derivative (dy/dx) and a function of x and y. The equation is:
Solving for C, we get:
1 = -1/(2(0)^3 + C)