The number of students in a school who have heard a rumor at time t hours is modeled by the function P, the solution to a logistic differential equation. At noon, 50 of the school’s 500 students have heard the rumor. Also at noon, P is increasing at a rate of 20 students per hour. Which of the following could be the logistic differential equation?

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Q: a. Classify and solve the first order differential equation y' = /2 +e'.

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Q: Obtain the general solution of the Logistic differential equation dP P - p? dt

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Q: Calculate whether the differential equation is exact or not and Find the general solution.

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Q: Which of the following is a Linear differential equation ?.

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Q: Find the order of the differential equation. And check if it is linear or nonlinear.

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Q: y = Ax2 + Be-* Find the differential equation by eliminating the arbitrary constants. *

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Q: Is the logistic equation a linear differential equation?

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Q: Solve the differential equation when = 5(10 – P) if P = 2 when t = 0.

A: Solving the problem by solving the diff equation.

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Q: . Solve the following Exact/Inexact Differential Equation.

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Q: y = C1e2" + C2e¬*

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Q: What do you mean by an implicit solution of a differential equation?

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Q: у- бу(100 - у) (y(0) = 20 %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.