5. Newton's Law of Cooling states that if an object with temperature T(t) is placed in a room with ambient temperature T,, then T(t) obeys a differential equation of the form T'(t) = k(T – T.), where k is a constant depending on the physical properties of the object. Suppose that you put a pot of stew, initially at 90 degrees Fahrenheit, into a 35-degree refrigerator. (a) What is the temperature T(t) of the stew after t minutes? (b) Suppose that after half an hour, the stew is at 70 degrees Fahrenheit. What is the constant k in our problem? (c) How long will it take for the stew to cool to 50 degrees Fahrenheit?

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Q: 9 Find the general solution to the differential equation y' where x > 0. y = +C

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Q: 5. In the given differential equation, eliminate the arbitrary constant. SHOW YOUR COMPLETE AND…

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Q: 2 (y+ 1) da- ydy = 0

A: Explanation of the answer is as follows

Q: 3. Find the differential equation associated to the equation: y = C₁x²e³* +C₁xe¹ +C₁e¹*

A: Note:- Since you asked multiple Questions ,As per our policy we can solve first question  for you…

Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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Q: A goat that weighs 6 pounds at birth gains weight at the rate (a) Find the particular solution of…

A: Solution is given below:

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Q: 1. Describe the solution of the differential equation ydx – 2xy dy = 0.

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Q: 2 Q-8 If y = 2[e2¤ + 3ln[x + (e² + 1)²]]´ then show that the value of the first order differential…

A: Use the formula a+b2=a2+2ab+b2, to expand the equation y=2e2x+3lnx+ex+122.…

Q: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

Q: determine the general solution to thegiven differential equation. y′′′ − y′′ + y′ − y = 0.

A:

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: 9. The rate at which a baby bird gains weight is proportional to the difference between its adult…

A: In the question it is asked to calculate rate of change of weight for the bird with age.

Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+y)dy=0, we let the substitution dw =- (Note: We use…

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Q: B/ Find solution for the homogenous differential equation below: dy x² +y² dx 2хy

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A: Answer:

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A: The given solution is y= c1e2t+c2e−3t.

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Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C

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Q: Q-8 If y = 2 [e2" + 3ln[x + (e + 1)²]]´ then show that the value of the first order differential…

A:

Q: 1. Find the general solution to the differential equation: y" = 4y' = 12y = tet

A: Given differential equation

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A: Given differential equation y' - 3yx = x4y13

Q: 1. y'- = xy2

A: Solution is given below:

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A:

Q: (5) Find the general solution for the exact differential equation (x² – 4xy – 2y2)dx + (y? – axy –…

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Q: What is the general solution of the first order differential equation a csc (2) - B| da + a dß = 0…

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A: Differential equations

Q: 3. a) Use the substitution u = -x+3y to solve the differential equation. -x+3y)y'= 1 b) Clearly…

A: After substitutions, separate du and dx.

Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy=0, we let the substitution dw =- (Note: We…

A: Given differential equation is 4(3x + y - 2)dx - (3x + y)dy = 0

Q: 5. Given a differential equation y ln x In y dx + dy = 0, find an expression that when multiplied on…

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Q: 1)a) Find the general solution of the differential equation (y')3 – y*(y + xy') = 0

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A:

Q: What is the order of the following differential equation  y' - y^2 + y^{(3)} =0

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Q: 5 Find the general solution to the differential equation y - where x > 0. y = +C

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Q: 3. The rate of decay in the mass, M, of a radioactive substance is given by the differential…

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Q: If y=3 when x=0 and y'=4 when x=0, determine the particular solution of this initial conditions,…

A: The given differential equation is                                                   y''-2y'-3y=0…

Q: 2. Determine the general solution of the given Differential Equation (x2 – xy + y?)dx – xydy = 0 - -

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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