The population, P(t), of a town increases as the following equation: P(t) = 500ekt. What is the value of k if the initial population has become 4000 in 2 years?

Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

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Q: Q13. Use Variation of Parameters to solve the DE y" – 4y =

A: Given: y''-4y=e2xx

Q: 3. Nevada's population in 1990 was 14.2 million and can be modeled by y = 14.2e0.0079t where t is…

A:

Q: solve for y in terms of t or x, as appropriate ln y = 2t + 4

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Q: Find the general solution to y"(t) = t1² – 3t* + e' – nsin (at). Show all steps

A: y"(t)=t12-3t4+et-πsin(πt)d2ytdt2=t12-3t4+et-πsin(πt)

Q: Suppose a cheetah is dashing due north at a rate of 30 m/s toward a popular watering hole, and a…

A: We need to find x(t),y(t),r(t) in the above question.

Q: Q12: What is the formula of The general solution for a D.E. with variable coefficients about…

A: Given x0 is an ordinary point of the differential equation.

Q: Given a cooling coefficient y of 0.1, how long does it take water at 20°C to freeze (reach 0°C) in…

A: Newton's law of Cooling is used

Q: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to…

A: From Newton’s Law of Cooling, we know that T(t) = Ts + Cekt Given C = 100, k = 0.1 Consider freshly…

Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: Q4: Solve the initial value problem: ty = 2y +t %3D

A: The general solution is, y = y(t) = t³ + t²•C, where, C is the constant of integration.   The…

Q: O Use the bisection method to numerically solve the nonlinear equation 1.5 f(x) = 40x3 – 875x+35000…

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Q: . It is known from past experiments that the height in feet of a certain plant after t months is…

A:

Q: the decay of 10 grams of a substance is given by the equation A=10(0.76)t where t is in hours.how…

A: To use the exponential model for decay to determine the required time .

Q: A. Solve the following DE by using exact equation method: y = x- y,

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

A:

Q: A. Solve the following DE by using exact equation method: y = x - y,

A: The given differential equation is dydx=x-y ⇒x-ydx-dy=0 ⇒M=x-y and N=-1⇒∂M∂y=-1 and ∂N∂x=0⇒∂M∂y≠∂N∂x…

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: Q1:- A) solve the following D.E x + x*)»' -3y = 0 1 x?y" + В):- у" + у' — бу %3 8e3х

A:

Q: A population of bacteria is growing according to the equation P(t) 1800e 0.09t. Estimate when the…

A: The population is given as a function of time. So put the population to get the answer.

Q: The population of a city can be modeled by P(t) = 24e0.0st thousand persons, where t is the number…

A:

Q: (i) A business manager determines that t months after production begins on a new product, 6t2 + 5t…

A: Given: P(t) = 6t2 + 5t(t + 1)2 To Find: limt→∞P(t).

Q: Solve the equation of change df/dx = 3 if the initial value of f is 7. a. f = 4x + 8 b. f = 3x + 7…

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Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A:

Q: 9. Solve for y, showing all work: 12x – 4y = 20

A: Using algebraic operation

Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: dy Solve the initial-value problem for y as a function of 2. (64 – x²) - 1, y(0) = 6 dr y =

A:

Q: he Solve the (D+D+1)y(x) = xe equation er y,(x)= (x -1)e* - (x-1

A: Differential equation

Q: If the power of the rocket handler is given by [(t – 11)(t² + 1) + 5(7t – 5)]e-0.5t Where t is the…

A:

Q: solve for y in terms of t or x, as appropriate.

A: given: lny=-t+5 we have to solve for y in terms of t or x, as appropriate

Q: It is easy to check that for any value of c, the function y = ce-2 + e- is a solution of the…

A: Ans:  We have to solve                y'+2y=e-x; y -1=5       We have to find C  for the solution of…

Q: A population of bacteria is growing according to the equation   P(t)=1550e^0.06t, where t is the…

A:

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: Q4) Use the Newton- Raphson method, with 1.5 as starting point, to find solution of f(x)= x-2sinx.

A: Given function f(x)=x-2sinx. The objective is to find the solution by using Newton-Raphson method…

Q: Find L{e*(t-1)}

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Q: Between 2005 and 2009, the percentage of people who own a home has changed drastically from state to…

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Q: Solve the follawing D ·E. 2. y²dx + (3xy +y²-1) dy =0

A: Please refer the attached image for complete solution.

Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

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Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

A:

Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: B- Solve the D.E.: y--e* = 0, y(1)=1 .

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Q: The following equation represents the growth of bacteria in a particular food product, where t…

A: Given, the number of bacteria function f(t) = 700e0.1t , where t is time in days. When the bacteria…

Q: Find the value of k so that the value of (2y - 1) dy is 10.

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Q: . A woman saved GH¢ 30,000 in a bank A, whose rate was x % per annum and GH¢ 20,000 in another bank…

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Q: For the linear equation y = 6.6 + 8.lx If x increases by 8, what is the resulting change in y?

A: Given: Interpretation of slope: For every one unit increase in x, the predicted value of y…

Q: Find a general solution to the given equation for t<0. 1 26 y"(t) - '(t) +

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Q: Find the general solution of the equation 4y'' + 4y' + y = e-t/2

A:

Q: y+1 =xy- all selutions ?

A: Given y+1=xy'-y'2

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

A:

Q: Apply Variation of Parameters to find the general solution. e* у"- 2у'+ у 3 1+x?

A: Given y''-2y'+y=ex1+x2