Find two positive numbers whose product is 64, and whose sum is a minimum. Solution must show the application of differential calculus.

Q: Determine the function if it is a solution to the differential equation or not.

A: Given function is a solution of the differential equation. This is a complimentary solution along…

Q: Describe how to determine whether a function y = f(x) is a solution of a differential equation.

A: We can determine whether a function y=f(x) is a solution of a differential equation by plugging in…

Q: How Three Functions of Wronskian are used to Find the Homogeneous Linear Differential Equation Whose…

A: Let's consider two function y1(x) and y2(x) are the linearly independent solution of y'' + p(x) y' +…

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters, and 60…

A: Given: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters and…

Q: The basic idea of optimization is that we have a quantity (represented by a function), and we need…

A: The basic idea of optimization is to find the maximum or minimum of a function using the different…

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A: Given that,The path of a basketball is given byy=2.12+2.01x-0.38x2, 0≤x≤4.6wherex is the horizontal…

Q: An ant is standing at the point (1,1,3) on the surface of a bowl with equationz=x^2+…

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Q: What are the rules or theorems that you may use to identify the difference between linear and…

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Q: Every homogeneous linear differential equation has solution. Select one: True False

A: Select one

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: The roots of an auxiliary cubic equation are m1=-1 and m2=m3=-5. What is the corresponding…

A: We have given the roots of an auxiliary cubic equation ,  m1 = -1  , m2 = m3 = -5 Thus , Auxiliary…

Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

Q: Solve the differential equaton 2x2dy=(x+y)2dx

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Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

Q: Find the explicit solution of the separable equation

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Q: of the differential equati

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Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

Q: y(4) + 8y″ + 16y = 0

A: Given, y4+8y''+16y=0

Q: 5

A:

Q: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: Two bicyclists begin a race at 8:00 a.m. They both finish the race 2 hours and 15 minutes later.…

A: Let f(x) and g(x) be the function of positions of these two bicyclists. Using the mean value…

Q: Decide if the differential equations whose slope fields are shown below involve only x, only y, both…

A: To Find: Decide if the differential equations whose fields are shown above involves only x, only…

Q: Determine whether the given equations in standard form and differential form are SEPARABLE,…

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Q: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

A: Given, a hollow cylinder has a radius (R) of the outer surface, radius(r) of the inner surface and…

Q: The dimensions of a closed rectangular box are measured as 80 centimeters, 60 centimeters, and 100…

A: Let the dimensions of a closed rectangular box are: Length=L=80 cmWidth=W=60 cmHeight=H=100 cm And…

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: What is the importance of the auxiliary equation in the determination of the solutions of…

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Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: V9.22

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Q: 4.3√√√7

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Determine how solutions of the diferenciaseparable variáveis ​​variable differential equations…

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Q: /y' + 10 = 0, y(0) = 2 and y'(0) = 4 %3D %3D

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Q: Use a linear approximation (or differentials) to estimate the number V100.5

A: To find 100.5Let y=xLet x=100 and ∆x=0.5⇒y=100y=10Differentiate…

Q: State whether the given differential equation is linear or non-linear, ordinary or partial. Identify…

A: Consider the differential equation  y'+y=x2−2             ......(1)

Q: Solve the differential eguation 3-

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Q: ... Find the general solution of the system of linear differential equations (expr83s your answer in…

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Q: Which differential equations are called autonomous?

A: we have to tell which differential equations are called autonomous.

Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

Q: The side if a square floor tile is measured to be 4 inches, with a possible error if 1/32 inch. use…

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Q: Form the second-order differential equation using the parametric definition of y = asin0, x = acos0

A: Calculate dydθ and dxdθ first. Then calculate dydx, d2ydx2 and simplify to get the differential…

Q: Explain numerical approximation of solutions of systems of differentialequations?

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Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

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Q: Sketch one direction field for the differential equation. Then use it to sketch three solution…

A: Consider the differential equation:

Q: using partial differential equ

A: Charpit's auxiliary differential eqs are

Q: Can you give me one real life problem about integration?

A: Real life problem about integration Integration: integration is a method where we add the slices to…

Q: find all solution of z   sinh(2z)=-1

A: Consider the provided equation, sinh2z=-1 Find all solution of z. Apply the trigonometric…