Q 04: x(1-x*) (a) Using natural logarithm find y' of v=-* ) (b) find y"=" if y = In(x+V1+x² ) and y = In (In (tan x)) d'y dx

Q: A population of a certain rare species of tigers is modeled by the differential equation * = N(0.1 –…

A: For the solution of the problem follow the next steps.

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: A normal is drawn at a point P( x,y) of a curve, it meets the x-axis at Q. If PQ is of constant…

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Q: Find the differential equation corresponding to y=a cos (logx) +b sin(logx) or y=A sin (logx)…

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Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

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Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

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Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Consider a population of marine fish in a reef with and intrinsic growth rate of 0.5 per year and a…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Consider the logistic differential equation = ry(1 – ) with r, K > 0. This DE has a stable…

A: We will form the iteration formula for the Euler's method, which will turn the continuous dynamic…

Q: The logistic model can also be changed by incorporating a constant continuous rate of decrease, such…

A: Consider the given equation. dPdt=kP1-PA-H Put x=PA in the above equation. dxdt=1AdPdt Put all the…

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

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Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: When predicting population growth, demographers must consider birth and death rates as well as the…

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Q: Solve the differential equati on. dz (log x) = –(log z) dx X

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Q: A murder of crows in the wild is observed to double its population in one year. However, in…

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Q: Find: (a) particular solution of the logistic differential equation that describes the growth of…

A: The logistic differential equation that describes the growth of the population of wolves in some…

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

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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…

Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: Q19// Solve the partial differential equation du = Iny sin-x given that дхду = cosx when y-0 and u=y…

A: Initial value problem are those problem in partial differential equation in which initial condition…

Q: The total number of reported cases of an illness in a large city tt days after the start of an…

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

Q: Find the differential equation corresponding to y=a cos(logx) +b sin (logx) where a and b are…

A: For a given solution having N constants , we have to differentiate the given solution for N times to…

Q: dy = ky| 1- dx L)

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Q: The logistic equation is the autonomous differential equation: dN =r· N [ 1 dt (1-#) K Where r and K…

A: Solution for (1 a): When N is much smaller than K, the fraction NK is negligible, as it will be much…

Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: Let f be a function with f (3) = 1 such that all points (x, y) on the graph of f satisfy the…

A: This is Separable differential equation

Q: Suppose that a hare starts at the origin (0, 0) and runs with speed Vh along the y-axis toward a…

A: This question is from differential equation.

Q: Let k represent the growth constant for a certain bacteria, which grows at a the amount at that…

A: let the population of the bacteria after time t =y  it is given that;  growth rate ∝ amount at that…

Q: Birth and death rates of animal populations typically are not constant; instead, they vary…

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Q: 8) A bank pays interest to depositors at the rate of r percent per annum, compounded continuously.…

A: Note-  According to Bartleby guidelines, we are supposed to do only one question. If you want more…

Q: O A red-hot steel rod is suspended in air which remains at a constant temperature of 24°C. Find a…

A: As given that there is no change in temperature of rod with respect to time and it is constant and…

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: Here is the Answer and Explanation

Q: - Find dy/dx for y = log2(1 – sin³ (3x²) %3D

A: Use the chain rule to differentiate the given function.

Q: Find dy/dx for following: 1- Y= sec\x 2- Y= 2Vx X 3- Y= log2 8

A: We can make it easier for you.

Q: Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional…

A: Total number of people in the village are =800000. No. of people who have heard the news after t…

Q: Find dx if 2 siny dy 3 Log (y1)

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Q: In a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground…

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Q: At a time denoted as t = 0 a technological innovation is introduced into a community that has a…

A: Given information: Given that at a time denoted as t = 0 a technological innovation is introduced…

Q: Let y = 5(square root x) Find the change in y. Delta-y when x = 5 and delta-x = 0.1 Find the…

A: The given function is y=5x. We need to find ∆y when x=5 and ∆x=0.1. Also, to find dy when x=5 and…

Q: Let f(t) be the balance in a savings account at the end of t years. Suppose that y = f(t) satisfies…

A: Given differential equation:- y'=0.04y+2000

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

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Q: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: Let P(t) be the number of bacteria present at time t.Given that the growth rate is proportional to…

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

A: The given differential equation is dydt=825y54-y   with  y0=1. Solve the above differential equation…

Q: The implementation of a good harvesting policy for fisheries is crucial to ensure a sustainable…

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