Write a differential equation that models the given situation. The stated rate of change is with respect to time t. (Use k for the proportionality constant.) A news story is spreading within a city of fixed population N. The rate of change of the number y of individuals who have heard the story at time t is proportional to the product of the number of individuals in the population who have heard the story, and the number of individuals who have not yet heard the story. dy dt

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A: Area , A = ∫∫R dydx or  ∫∫R dx dy.

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A: I=∫ 3+x+4ex dxI=∫3 dx +∫x dx +∫ 4ex dxI=3∫dx +∫x dx +4∫ ex dxI=3x+x22+4 ex +C

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A: use the cross product and determinant  for solving the area.

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A: Solution is given below:

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A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

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A:

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Q: Find the solution of the following Differential Equations 8) y-2y'+2y = 2e" cos(x)

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Q: 1 )dx 4.

A: We will use substitution method to solve question 4.

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A: To find the x values where the function is not continuous and not differentiable.