bdh2991 said:Homework Statement
dP/dt=P-P^2
Homework Equations
The Attempt at a Solution
I know you can separate this and after i did that and did my partial fractions i got
t + C = ln(P) + ln(1-P) but i don't know what to do from here i figure you take the e of both sides at some point but i never ended up with the right andswer please help
bdh2991 said:i'm not seeing where the sign error is coming from...for my partial fractions i did
A/P + B/(1-P), then getting rid of the denominators i get A(1-P) + Bp = 1
solving for A and B i get A=1, B=1
so wouldn't it be ln(P) + ln(1-P)??
the only thing i could think is that it should be A(1-P) - BP
but i don't really understand how it could come out as a subtraction
bdh2991 said:i'm not seeing where the sign error is coming from...for my partial fractions i did
A/P + B/(1-P), then getting rid of the denominators i get A(1-P) + Bp = 1
solving for A and B i get A=1, B=1
so wouldn't it be ln(P) + ln(1-P)??
Separation of variables is a method used to solve certain types of differential equations, where the equation can be separated into two or more simpler equations by writing the variables as separate functions and then integrating each side separately.
Separation of variables is typically used when the differential equation is of the form y' = f(x)g(y), where the variables x and y can be separated into two different functions.
The general process for solving a differential equation using separation of variables is to first write the equation in the form y' = f(x)g(y). Then, separate the variables by dividing both sides by g(y) and multiplying both sides by dx. Next, integrate each side separately, with respect to x and y. Finally, solve for y to obtain the solution to the differential equation.
Yes, there are certain types of differential equations that cannot be solved using separation of variables, such as non-linear equations or equations with non-constant coefficients. It is important to check if the equation is suitable for separation of variables before using this method.
Yes, separation of variables can also be used to solve higher order differential equations, where there are multiple variables involved. However, the process becomes more complex and may require additional techniques such as substitution or integration by parts.