- #1

prolong199

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y'=(y-2)^2(y-4) if y(0)=3, the limit of y(t) as t goes to infinity is?

a) infinity

b) 4

c) 2

d) 0

e) -infinity

thanks.

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- Thread starter prolong199
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In summary, the differential equation y'=(y-2)^2(y-4) with initial condition y(0)=3 has a limit of 2 as t goes to infinity. This can be seen by graphing y' as a function of y and observing that as y approaches 2, the speed of movement along the y-axis decreases until it reaches 0 at y=2, indicating that y will tend towards 2 or reach and stay at 2. The approach to finding the function y(t) may require integration, but the overall process is not too complex.

- #1

prolong199

- 12

- 0

y'=(y-2)^2(y-4) if y(0)=3, the limit of y(t) as t goes to infinity is?

a) infinity

b) 4

c) 2

d) 0

e) -infinity

thanks.

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prolong199

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- 0

- #3

AKG

Science Advisor

Homework Helper

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teclo

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prolong199 said:

y'=(y-2)^2(y-4) if y(0)=3, the limit of y(t) as t goes to infinity is?

a) infinity

b) 4

c) 2

d) 0

e) -infinity

thanks.

the first thing you'd want to do is get y as a function of t.

whoops, i missed your second post. yes, you want to solve for the function y{t} and take the limit as it goes to infinity. you have the right approach, the integration just gets a little messy (but not bad really, assuming that your functions are really multiplied by each other and not one to the power of the other)

Last edited:

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves variables, constants, and mathematical operations, and is used to model natural phenomena and physical systems.

Boundary conditions are specific values or relationships that must be satisfied by the solution of a differential equation at the boundaries of the domain. They help to determine a unique solution to the equation.

To solve a differential equation with boundary conditions and limits, you first need to identify the type of differential equation (e.g. first-order, second-order, etc.) and the type of boundary conditions (e.g. Dirichlet, Neumann, etc.). Then, you can use various techniques such as separation of variables, integration, and substitution to obtain a solution that satisfies the given boundary conditions and limits.

Initial value problems involve finding a solution to a differential equation that satisfies given initial conditions, while boundary value problems involve finding a solution that satisfies given boundary conditions. In other words, initial value problems have conditions at a single point, while boundary value problems have conditions at multiple points.

Differential equations with boundary conditions and limits are important because they allow us to model and understand real-world problems and phenomena. They are used in various fields such as physics, engineering, economics, and biology to make predictions and solve practical problems.

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