Is this differential equation separable?

In summary, the given equation is separable and can be solved using the laws of logarithms. After applying the log law and factoring out t^4, the equation can be further simplified to t^3*(5t)*ln(s) + 8t^4.
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  • #2
Yes, it is separable. Use the laws of logarithms. ln(s^(5t))=(5t)*ln(s). Now separate it.
 
  • #3
how do you go on separating it after that? my guess would be:

the 8t^4 confuses me
 
  • #4
What do you get after you apply the log law? Factor out the t^4. The question is just asking whether it's separable.
 
  • #5
t^3*(5t)*ln(s) + 8t^4
 
  • #6
-EquinoX- said:
t^3*(5t)*ln(s) + 8t^4

Well? Keep going. t^3*5*t=5t^4...
 

1. What is a separable differential equation?

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.

2. How do I know if a differential equation is separable?

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.

3. What are some examples of separable differential equations?

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).

4. How do I solve a separable differential equation?

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.

5. Can all differential equations be solved by separation of variables?

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.

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