2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] , where Ĥ is a 1D Hamiltonian with V̂=V0 (constant)   (d) [Â,B̂], where  = d^2/dx^2 + x   and    = 1

Q: dx/dt = 2 and y=x^3, what is dy/dt when x=-4,2,6

A:

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

A:

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: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

A:

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

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Q: Find the differential dy of y=√x. Show complete solution

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: Integrate sin 6y sec 3y dy from limit 0 to π

A:

Q: Ily approximate the differential dy when x changes from 64 to 64,07 Y

A: Since the student has posted multiple questions and mention to solve question numbers 1 and 2. But…

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. [x x cos…

A:

Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

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Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: Find the differential equation of the family of circles of fixed radius r with center on the x-axis.

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Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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Q: Find the differential equation of all sphere of radius 5 having their centers in the xy plane

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Q: From the partial differential equation by eliminating the arbitrary functi on s f and g from = z =f…

A: Given: z=fx+ct+gx-ct

Q: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

A:

Q: te dt.

A:

Q: Classify the first order differential equation .9 y = (y – 2) X اخترأحد الخيارات Separable…

A:

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A: Solution:-

Q: 1 point) Find dy/dx by implicit differentiation. 2cos(x)sin(2y)=−4 dy/dx=dy/dx

A: It is implicit differentiation.

Q: Prove first that sinx siny dx - cosx cosy dy =0 is an exact differential equation then determine its…

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Q: integral from -1 to 1 of arccos (y) dy

A:

Q: 4 Use Gaussian Integration (4-point form) to approximate x2sin(x)dx

A: Using 4-point formula the given integration is solved.

Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

A: The given differential equation is dvdt=-kvn, where k>0 and n are constants and v(0)=v∘. At t=0,…

Q: Form the partial differential equation by eliminating arbitrary function from z=exf(x−y)z=exf(x−y)

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Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

A:

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: Explain in detail the use of partial differential equations in the application of heat transfer

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Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: Find the Differential Equation of the Families of Circles with center (2,k) and with radius r.

A:

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: Find two positive numbers whose product is 64, and whose sum is a minimum. Solution must show the…

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Q: Circles with center on the line y = x

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Q: 5. Suppose that (b) field plot. dy dx = (4- y) (5-y). Find the equilibria of this differential…

A: 5. Given dydx=4-y5-y   (a) To find: the equilibria of the equation. (b) To classify: each equilibria…

Q: What are the new limits of integration if apply the substitutior u = 6x + t to the integral sin (6x…

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Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: What are the new limits of integration if apply the substitution u = 4x + t to the integral / sin…

A: We have to change the limit.

Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: 4. What is the total differential dW given W In(x+y +z)? 5. A light is hung 15ft above a straight…

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Q: The Derivative az/ax of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x)…

A:

Q: In 3 | (1-x)e"dx ах In

A: Consider the given integral

Q: Consider the differential equation = 5 - y. In a coordinate system with window [-3,11] by [-4,10],…

A: Consider the equation

Q: Find the differential equation of the family of spheres of radius r with Centre on the xy-plane

A: General form of the equation of the sphere with radius r and center on the xy plane is given by…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.