Slimsta said:i got it by plugging the slope into m in the equation y=mx+b
Dick said:That makes no sense whatsoever. I think you know that. They want the y intercept of the curve. I think you have to solve for the curve. Whatever happened to the "separable equations" part of your post title? Shouldn't you separate dy/dx=(-2/y^3) and solve it??
Slimsta said:okay so i get dy/dx=(-2/y^3)
==> y^3 dy = -2dx
==> (y^4)/4 = -2x + C
==> y= sqrt4(-8x + 4C)
now what do i do?
rock.freak667 said:They gave you a point that it passes through, so find, the constant C.
Office_Shredder said:So you have a curve passing through the point given, with the slope that they require. What does the question tell you to do with it?
Separable equations are a type of differential equation where the variables can be separated into two different functions that are multiplied together. This allows us to solve the equation by integrating each function separately.
To solve a separable equation, you first need to separate the variables into two functions. Then, integrate each function separately with respect to its variable. Finally, combine the two solutions and solve for any constants that may be present.
Solving separable equations allows us to find the general solution to a differential equation. This can be useful in many fields of science and engineering where differential equations are used to model real-life phenomena.
Yes, there are some special cases where separable equations can be solved using specific methods. For example, exact equations can be solved using the method of integrating factors. Additionally, some equations may require substitutions or other techniques to be solved.
Yes, separable equations can be used to model many real-life situations, such as population growth, radioactive decay, and chemical reactions. By solving these equations, we can make predictions and understand the behavior of these systems.