Answer:
Step-by-step explanation:
The given differential equation is y' = (36xy)^2.
To solve this, we can use separation of variables. We start by separating the y and x terms and then integrating both sides:
dy/y^2 = (36x)^2 dx
Integrating both sides, we get:
-1/y = 4x^3 + C
where C is the constant of integration. We can then solve for y by taking the reciprocal of both sides:
y = -1/(4x^3 + C)
This is the general solution to the given differential equation. It includes the constant C, which can be determined by using an initial condition.
In summary, to solve the given differential equation, we used separation of variables and integration to obtain the general solution y = -1/(4x^3 + C), where C is the constant of integration. This solution can be used to find the value of y for any given value of x and C.