Question

Asked May 19, 2019

148 views

Consider the differential equation

dy/dt = y−y2.

Given that y(0)=0.5, solve the differential equation by separating the variables and integrating. Given that

y→L as t→∞,

for some constant L, find the value of L.

*Hint: You may use the fact that*

Step 1

To find the expression for y(t) and find the limit y(t) as t tends to infinity

Step 2

Separate the variables and use partial fractions. As the denominator is not defined at y=1 , we need to discuss the cases y<1 and y>1 separately

Step 3

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: How can I get the result?

A: We used a calculator to find the values for the table. And rounded each value to 4 decimal places. ...

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

Q: If the formula describing the distance s(in feet) an object travels as a function of time(in seconds...

A: The distance s(in feet) an object travels as a function is s = 100 + 160 t -16t2.It is known that, t...

Q: Let (0 ifx-5 f(x) 0 ifz 4 and 9(x)-f(t)dt 5 Determine the value of each of the following (d) g(5) (e...

A: The functions are given as

Q: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line tang...

A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the...

Q: Please sketch this by hand! And show all your steps as im doing my best to fully understand the proc...

A: (A) The function has an absolute maximum but no local maximum. This means the graph is strictly incr...

Q: Answers for 10-12

A: We will solve Q-10

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by...

A: Consider the given function: