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B. Direction: Find the differential equation of the family of curves described. 1. Find the differential equation satisfied by the family of parabolas having their vertices at the origin and their foci on y-axis. 2. Find the differential equation of the family of circles having their center on the y-axis. 3. Find the family of curves of straight lines with slope and y-intercept equal. 4. Ellipse with center at the origin. 5. Circles with fixed radius "r" and tangent to the x-axis.

B. Direction: Find the differential equation of the family of curves described. 1. Find the differential equation satisfied by the family of parabolas having their vertices at the origin and their foci on y-axis. 2. Find the differential equation of the family of circles having their center on the y-axis. 3. Find the family of curves of straight lines with slope and y-intercept equal. 4. Ellipse with center at the origin. 5. Circles with fixed radius "r" and tangent to the x-axis.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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B. Direction: Find the differential equation of the family of curves described. 1. Find the differential equation satisfied by the family of parabolas having their vertices at the origin and their foci on y-axis. 2. Find the differential equation of the family of circles having their center on the y-axis. 3. Find the family of curves of straight lines with slope and y-intercept equal. 4. Ellipse with center at the origin. 5. Circles with fixed radius “r" and tangent to the x-axis.
Transcribed Image Text:B. Direction: Find the differential equation of the family of curves described. 1. Find the differential equation satisfied by the family of parabolas having their vertices at the origin and their foci on y-axis. 2. Find the differential equation of the family of circles having their center on the y-axis. 3. Find the family of curves of straight lines with slope and y-intercept equal. 4. Ellipse with center at the origin. 5. Circles with fixed radius “r" and tangent to the x-axis.
D. Direction: Answer the following mixing problem using separation of variables. A typical mixing problem involves a tank of fixed capacity filled with a thoroughly mixed solution of some substance, such as salt. A solution of a given concentration enters the tank at a fixed rate and the mixture, thoroughly stirred, leaves at a fixed rate, which may differ from the entering rate. If y(t) denotes the amount of substance in the tank at a time t, then y'(t) is the rate at which the substance is being added minus the rate at which it is being removed. The mathematical description of this situation often leads to a first-order separable differential equation. Problem: A tank contains 20 kg of salt dissolved in 5000L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour?
Transcribed Image Text:D. Direction: Answer the following mixing problem using separation of variables. A typical mixing problem involves a tank of fixed capacity filled with a thoroughly mixed solution of some substance, such as salt. A solution of a given concentration enters the tank at a fixed rate and the mixture, thoroughly stirred, leaves at a fixed rate, which may differ from the entering rate. If y(t) denotes the amount of substance in the tank at a time t, then y'(t) is the rate at which the substance is being added minus the rate at which it is being removed. The mathematical description of this situation often leads to a first-order separable differential equation. Problem: A tank contains 20 kg of salt dissolved in 5000L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour?
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