The temperature inside a room is given by T(x, y) = x4 + y4 – 4xy+4. Find and prove the location(s) where the lowest (coolest) temperature occur inside the room.

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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A: We have to find the general solution of the differential equation by using a variation of parameter…

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A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

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Q: \ Find y (0.24) using Runge-Kutta method with h = 0.08, y (0) = 1.3456 %3D f(x, y) = x + y?

A: Given equation is dydx=y'=f(x, y) where f(x, y)=x+y2 and step size h=0.8Also, yx0=y0 where x0=0 and…

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A: Given differential equation is xy2dx+exdy=0

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

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Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: Use Variation of parameters to find the solution of the initial valuue problem 3y = t², y(1)

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Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

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Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

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Q: Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0

A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

Q: when

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

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Q: Use the explicit Euler and Runge- Kutta methods to estimate y(2) if y(t) is a solution to y' = 1/…

A: For calculations only take t as x. Given y′=1x2+y, y(0)=1, h=0.2, y(2)=?Here, given is…

Q: Find the total differential. 4x + y w = 2z - 8y |

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Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

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Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: -2x 11/E valuate the integral 2 é V1-

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Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* – x)dy = 0

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Q: Use Separation of Variables to solve the initial value problem. dy : (1 + y²) tan z, y(0) = v3 xp

A: solution of the given equation is tan-1y + log(cos(x)) = π3 detailed solution is given below

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Q: Given y = V4x+5, find the differential dy when x = 7 and dx = 0.3. Round your answer to three…

A: Take derivative with respect to x and put the given values.

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

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A: The given equation is; t2y" - 5ty' +7y= t

Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: A detailed solution is given below.   (As per our guidelines, we have to solve only 1st question)

Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

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Q: Determine the constant of integration of f (x) = S (15z* – 3x²) dæ if ƒ (1) = 4?

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Q: Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y »y(0) = 1 (h=0.01) .What is the error in the…

A: The solution is given as

Q: Given y = = V4x + 5, find the differential dy when.x 7 and dx = 0.3. Round your answer to three…

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Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.