Finding general solution for y(t): Very Difficult

In summary, the conversation discusses finding the function y(t) with the initial condition y(0) = 4000, using the given equation v = 20√10 x ((1+Ae^(t/√10))÷(1-Ae^(t/√10))) and the fact that A = -1 when finding the particular solution to satisfy the initial condition v(0). The terminal velocity is also mentioned as 63.246 m.s^-2. The conversation concludes with a question about integrating v(t) to find y(t) and determining the integration constant using the boundary condition.
  • #1
andrey21
476
0
Find y(t) assuming that y(0) = 4000


Homework Equations



This is what I know!


v = 20√10 x ((1+Ae^(t/√10))÷(1-Ae^(t/√10)))

and

A = -1 when finding particular solution to satisfy initial condition v(0).

Terminal velocity = 63.246 m.s^-2


The Attempt at a Solution



The question states to substitute the solution for velocity into th efollowing equation and solve for y(t).

y' = v

I don't really know where to start and have been trying numerous methods help desperatley needed. Thank You
 
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  • #2
You mean, the initial condition is v(0) = terminal velocity? If this is correct, then simply integrate v(t) to find y(t) and use the boundary condition to determine the integration constant. Also, I assume the "x" in your definition of v means "times"?
 
  • #3
Firstly yes the 'x' means times sorry bad formatting, second if that is the case how would I go about integrating v(t) to find y(t)?
 

1. What is a general solution for y(t)?

A general solution for y(t) is an equation that describes all possible solutions for a given differential equation. It includes a constant of integration and can be used to find specific solutions for different initial conditions.

2. Why is finding a general solution for y(t) difficult?

Finding a general solution for y(t) can be difficult because it involves a complex process of integration and solving for unknown constants. It also requires a strong understanding of differential equations and mathematical techniques.

3. What are some strategies for finding a general solution for y(t)?

Some strategies for finding a general solution for y(t) include separation of variables, using substitution or integration by parts, and using known solutions of simpler differential equations to solve more complex ones.

4. Can a computer program be used to find a general solution for y(t)?

Yes, a computer program can be used to find a general solution for y(t) by utilizing numerical methods or symbolic calculation tools. However, the accuracy and efficiency of the results may vary depending on the complexity of the equation.

5. How is a general solution for y(t) different from a particular solution?

A general solution for y(t) includes a constant of integration and represents all possible solutions for a given differential equation. A particular solution, on the other hand, is a specific solution that satisfies the given initial conditions for the differential equation.

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