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-EquinoX-
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Homework Statement
Is the following separable?
http://img90.imageshack.us/img90/3925/separable.th.jpg [Broken]
how do I know if it is?
Homework Equations
The Attempt at a Solution
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-EquinoX- said:t^3*(5t)*ln(s) + 8t^4
A separable differential equation is one in which the variables can be separated into two functions that involve only one independent variable. It can be written in the form of dy/dx = f(x)g(y), where y is the dependent variable and x is the independent variable.
A differential equation is separable if it can be written in the form of dy/dx = f(x)g(y). You can check if a differential equation is separable by seeing if the variables can be separated into two functions involving only one independent variable each.
Examples of separable differential equations include dy/dx = x/y, dy/dx = sin(x)cos(y), and dy/dx = 2x^2/y. These equations can all be rewritten in the form of dy/dx = f(x)g(y).
To solve a separable differential equation, you need to separate the variables and then integrate both sides with respect to their respective variables. This will result in a general solution, which can then be further simplified by applying initial conditions if given.
No, not all differential equations can be solved by separation of variables. Only certain types of differential equations, such as those that can be written in the form of dy/dx = f(x)g(y), can be solved using this method. Other techniques, such as substitution or using an integrating factor, may be needed to solve more complex differential equations.