If x = sin t and y = cos t then the co-ordinates of the stationary points are a:) (0,1) b) (1,0) c) (0,0) d) None of These

Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: 5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a…

A: We have to find out the potential difference at various points.

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: 10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you…

A: First we show that g(3)&gt;4 ,so g(3) does not belongs to [3,4]So we can not say that g(x) is in…

Q: Sketch the strophoid shown below. r= sec(0)- 2 cos(8), -<0 < x/2 1.0 1.0 0.5 0.5 -10 -0.5 0.5 1.0…

A: A strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the…

Q: From the Laplace Equation show that there exist solutions in the form X(x) +Y(y) + Z(z)

A:

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

A:

Q: Uxr + 3uyy = cos(x + y)u is second order, non linear, non homogeneous first order, linear,…

A:

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if ux = v, and u,…

A: Given u = x2-y2v = 2xy Then ux = 2xuy = -2yvx = 2yvy = 2x

Q: ) If ƒ(x,y) = 3x²y + cosy+ ysinx – e2x then verify fxy = fyx

A: fx and fy are the partial deferential of function w.r.t x and y respectively. Then fxy is the…

Q: Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many…

A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: 1- Verify the orthogonality properties of sines and cosines on the interval [—L, L] So, m #n *…

A: The first orthogonality property on the interval -L, L. ∫-LLsinmπxLsinnπxL dx =0,   m≠nL,   m=n…

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and -…

A: Given that the functions u and v are said to satisfy Cauchy Riemann equations if ux=vy   and uy=-vx…

Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: Express a general solution to 2x (1 — х)у" + (3 — 10х)у — бу %3D 0 Using Gaussian hypergeometric…

A:

Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

A:

Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: Assuming that the voltage may be described by the sinusoid v = K sin(wt + p), determi values of K, w…

A: Consider the given oscilloscope recording as shown below: And the given voltage is: Objective is…

Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

A:

Q: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

Q: 2. Let F(t) = (e' cos t) î+ (e' sin t)j+ek. a. Find symmetric equations of the line tangent to the…

A: Given:  F→t = et costi^ +et sint j^ +et k^  To Find:  Symmetric equations of the line tangent to the…

Q: Solve by theorems of linearity and translation. f(t) = cos t + sin t

A:

Q: (b) Utt = t>0, u (r,0) = 3 sin r, u (r,0) = 0, 0 0.

A:

Q: Let C be the shortest path that connects a to ni and I = J. (coshz – 1)dz. Then I=-sinh T+ T(i-1)…

A:

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

A:

Q: a2u a2u =4 at2 au(x,0) où 0 sxs2 with (0,t) = u(2,t) = 0, = 0, %3D %3D %3D at x if 0<x <1 2-х т u(x,…

A: utt =4 uxx               :  0≤x≤2 u0,t = u2,t =0utx,0 =0   ux,0 =x      : 0≤x≤12-x : 1≤x≤2

Q: 8. [M] Show that {1, cos t, cos? t,..., cos t} is a linearly inde- pendent set of functions defined…

A:

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: ▼ 3.1. Use Cauchy-Riemann equations to prove that ƒ(z) = z² is differentiable at z = zo E C.

A:

Q: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

A:

Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: 3.b) Eliminate the Ar bitrary Constants in the equation: ( 3.a) Eliminate the Arbitrary Conat anta…

A: We have to obtained differential equation of given curves.

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if ux = v, and u,…

A:

Q: Show that if the function f(x, y) = ecos-e-cosx, satisfies Laplace Equation.

A:

Q: 2.5.1. Solve Laplace's equation inside a rectangle 0SISL, 0SYSH, with the following boundary…

A: we search for the solution of the boundary value problem as a superposition of solution…

Q: • Verify that 3r is a one-parameter family of solutions of the DE ry + y = 3r. • Deduce a solution…

A:

Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

A:

Q: The functions cos r and cos- are linearly dependent (0, ) on

A: evident from the two curves that after zero in a positive direction the two graphs coincide with…

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: =y一;-T十;-一

A: Draw the family of these one parameter DE's of bifurcation.    Further, to solve these.

Q: 14. Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point. f(2) = Z b)…

A:

Q: Consider Y; = 0 + 0,X¡ + E¿, i = 1,2,..,n, e, - N(0,0), the cov(ô,Y) = %3D

A:

Q: 7. Let F = (2x sin(y)e", x² cos(y)e*, z² sin(y)e*). Find along the path c:T = (sin(t), t, cos(t))…

A: F=2xsinyez, x2cosyez, x2sinyez curlF=ijk∂∂x∂∂y∂∂z2xysinyezx2cosyezx2sinyez⇒curlF=0 So, F is a…

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.