6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, t), and the functions y,(t) = t, y2(t) = sint are solutions of the ODE y" + p(t)y' +q(t)y=0 0 < t < n a) Compute the Wronskian of yı, Y2. Are they linearly independent on the interval (0, n)

Q: Use Chain Rule to find given w = ds x2 – 2y + z2 and a = cos (st), y = -2s In t and z = s – - VE.

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Q: Consider the hyperbolic partial derivative equation Uzz = Uu – sin (x), rE [0, 1], t>0, with the…

A: Given,uxx=utt-sin x , x∈0,1, t&gt;0Boundary conditions: u(0,t)=ux(1,t)=0 , t&gt;0…

Q: Show that the two linearly independent solutions of xy" – y + xy = 0, x > 0 can %3D be obtained as…

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Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y),…

A: As per the policy, we are solving the first question. Please repost the question and specify which…

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A:

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: 6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, x), and…

A: Use the formula of Wronskian to determine its values. The functions are already given. Determine…

Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

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Q: 11. Show that U(x, y, z) = (x² + y² +z²) satisfies Laplace's partial differential equation + = 0.

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Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A:

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: 6. Let u (r, t) be the solution of the initial-boundary value problem ut = 9uzz 0 0, %3D uz (0, t)…

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

A:

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x,…

A: Topic:- calculus

Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: Let F(x, y, z) = (2x cos(y), e² – x² sin(y), ye²). (a) If possible, find all potential functions for…

A:

Q: Use Laplace transform to solve the partial differential equation: 8² y dy dx² at +xt where y(x,0) =…

A: Solution

Q: 6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, x), and…

A: Given differential equation is y''+pty'+qty=0 Given y1t=t and y2t=sint are the solutions of the…

Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

A:

Q: Use Laplace transform to solve the partial differential equation: d'y dy ox² at -+xt where y(x,0) =…

A: The given P.D.E is ∂2y∂x2=∂y∂t+xt where yx,0=0, y0,t=0 and yx,t is bounded for t&gt;0 and x&gt;0. To…

Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

A:

Q: 2. Find the linearization L(x, y, z) of f(x, y, z) = x² + xy + yz + 22 at the point (0, 1, 2).…

A:

Q: The differential operator Lis defined by d (e* 一 Ly = -e*y · - - dx dx (a) Determine the eigenvalues…

A: Given : Differential operator L is defined by…

Q: . Verify that the differential operator defined by…

A:

Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

A:

Q: 1. Determine the types of the following partial differential equatio: (a) 4upa - 4uæy + Uyy 4uxy (b)…

A: According to the guidelines I am answering only first question.

Q: Compute the first-order central difference approximations ofO(h^4) of t function of y at x = 1h =…

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Q: Let y1 (t) = e 2t cos (3t) and y2 (t) = e 2t sin (3t). The Wronskian W( y1, y2 ) (t) equals A. W(…

A:

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: 10. Show that if f is homogeneous of degree n, then r* fn + 2ryfzy + y° fy = n(n – 1)f(x, y). (A…

A: Suppose that f is a homogeneous of degree n. To prove that x2fxx+2xyfxy+y2fyy=nn-1fx, y. By Euler's…

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: Consider the vectors x(¹) (t) = ( ) and x(²) (t) = ( 6 ). 6t (a) Compute the Wronskian of x(¹) and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 26.Show that if p is differentiable and p(t) &gt; 0, then the Wronskian W(t) of two solutions of…

A: Given: [p(t) y′]′ + q(t) y = 0 W(t) = c/ p(t)

Q: Consider a regularizing term defined by where k!2* and the linear differential operator D is defined…

A: We are given the following regularizing term.                    ∫ℝN0DF(x)2 dx=∑k=0∞ak∫ℝN0DkF(x)2 dx…

Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: (1) Show that F(x, y) : (2x + y, x - y) is path independent and use the fundamental = theorem of…

A:

Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

A:

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

A:

Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: Use Laplace transform to solve the partial differential equation: o'y dy = dx² ôt where y(x,0)= 0,…

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Q: 1. For u(x, t) defined on the infinite domain of -o 0, solve ди with boundary conditions: u(x, t)…

A: Given ∂u∂t=-∂4u∂x4+e-x2-t Boundary conditions: u(x,t) and its first and second derivatives in…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: