(3) (1) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x>0 they know that S(x)=23 I+r+2x If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source?

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A:

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A: In this,we cam find the expression for the temperature using given initial temperature distribution.

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A: For statement

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A: Differentiate y=fx-at+xgx-at+x2hx-at with respect to x and t, to obtain ∂3y∂x3, ∂3y∂t3, ∂3y∂x2∂t and…

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A: For given statement

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A: (ii) Consider dCdt+0.06C=0⇒dCC=-0.06 dtIntegrating both sides we get⇒∫dCC=-0.06 ∫dt⇒log…

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Q: For the Initial Value Problem given below:

A: Given,                dydx+2y=2-e-4t, y(0)=1

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A: The logistic model is given by the below differential equation. dPdt=kP1−PM1−mP

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Q: Consider the IVP: x" +3(x')2 + 10tx = 0, x(0) = - 3, x'(0) = 2 Using the Euler method with a time…

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Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

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A: I have solved using two methods

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A:

Q: 3. Use an integrating factor to find the solution of the initial value problem. Give an explicit…

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A: .

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A: Find out the value of I after 1.5 seconds.

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A:

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A: Consider the following differential equation: 3x2y-lnx+3ydx-2lnx+xy-3dy=0 M=-2lnx+xy-3N=3x2y-lnx+3y

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Q: (a) The reaction to form an iodine molecule is a second-order kinetics rate of loss of iodine atoms…

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Q: Solve the partial differential differential by separation of variables 3 + 7 0. %3D

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Q: The Black-Scholes equation is an application of the parabolic partial differential equation (PDE)…

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Q: The initial concentration of phosphorous (C) in a waste water pond is 10' ppm, as against he…

A: we have dCdt+0.06C=0, C0=107 ppm we know that by Euler's method  yn+1=yn+hftn,yn where tn+1=tn+h we…

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A:

Q: 6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cmls…

A:

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0,…

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Q: At the time of t = 0 at 15 cm length (Δx=3 cm, Δt=0.4 s), one side of the rod is contacted with two…

A: This question is about application of integration

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Q: Example 10.33. Applying Euler's method to the equation dy/dx = hy, given y(x) = yo determine its…

A: We need to solve this problem using Euler's Method.

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Q: In the Four-Step Rule, which among the steps is the most important, upon which the foundation of…

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Q: 4. Find the explicit particular solution of the initial value problem give dy -уе , у(0) %3D 9 е 8x…

A: We will find the solution to the Differential equation.