9. A solution to a DE with arbitrary constants is known as a general solution. 10.The equation y' (e^x)(log y) is a linear DE.

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A: We have to find the differential equation to describe growth of population y(t).

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A: Consider the radioactive decay of an isotope is given by  and the solution of this differential…

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A:

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

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A:

Q: The isotope thorium-234 has a half-life of 24.5 days. (a) What is the differential equation…

A:

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A:

Q: What differential equation corresponds to an RC circuit with a resistor of R = 100 and a capacitor…

A:

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A:

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A:

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A:

Q: Suppose that you now have $10,000 and that you expect to save an additional $4000 during each year,…

A: Given that, You now have $10,000 and that you expect to save an additional $4000 during each year,…

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A:

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Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

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A:

Q: From the Newton's law of cooling, the cooling rate of a body is proportional to the difference…

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Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: a) Given half life= 58 minutes  So if initial value= C= 1 Then after 58 minutes A= 1/2=0.5 Using…

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A: Given the logistic differential equation is: y'=15600y1400-y…1 The standard form of a logistic…

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A:

Q: 4.y = C₁e-2x + C₂e³x

A:

Q: verify that the indicated function is an explicit solution of the given differential equation…

A:

Q: 3. x? = Axy + By: A and B are arbitrary constants

A: Given: x2=Axy+By, where A and B are arbitrary constants.

Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

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A: Given- A zircon sample contains 4000 atoms of the radioactive element 235U and 235U has a half‐life…

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A:

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A: We will find out the required solution

Q: dy = ky| 1- dx L)

A:

Q: 5. Verify that y = (x³ – x) log cx satisfies the differential equation (x³ – x)y' – (3x? – 1)y = x5…

A:

Q: 19.) [(ycoth y² )log°(sinh y² )dy

A:

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Q: Please Find the general solution to the differential equation x'''+x''+x'+x=0

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Q: An L-R-C circuit has the following differential equation: (q = charge on capacitor) q + 10 ġ + 100 q…

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Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

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Q: y' - 2x = -e-t; y(0) = 2

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Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

A:

Q: 41. The trough in Figure 3 (dimensions in centimeters) is filled with water. At time t = 0 (in…

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Q: Suppose a population P(t) satisfies logistic differential equation dP/dt=0.1P(1-(P/2000))…

A: SOLUTION-

Q: Given y" + (y)° + 5 = 0 is a differential equation with degree 3 and order 5 O TRUE O FALSE

A: Topic = Differential equation FALSE

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A:

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Given,  k = -0.283033 , let initial amount = C= 1 , final amount =A=0.5  We have to find t

Q: 8. Obtain the differential equation associated with the given function: y = Cx² + C².

A: Proceed as shown

Q: Show that solving the logistic differential equation results in the logistic growth function

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.