Which functions form the basis of solutions for the ODE y – y" – y" +y' (x) = 0? O {1, e ?, e², æe } O {1, e ", e", xe²} O {z, e", e¯ª, xe"} O {1, æ, e ", e*}

Q: @ Determine the directional derivative of F(x,y.z)= e*co5 ly) (1-2)² at the origen in thé directio…

A: This is a problem of vector calculus.

Q: -1 < x <0 The Fourier integral of f(x) = 1, 0<x<1 0, otherwise 00 (1 – cos(w)) sin(wx) dw lw 1. 00…

A: Given that fx=-1-1&lt;x&lt;010&lt;x&lt;10otherwise The Fourier integral of f(x) defined on -∞,∞ is…

Q: Find Vf at the given point. f(x, y, z) = 32³ – 2(x² + y²) z + tan '(4xz), (0, 2, 3) Vf\(0,2,3) f(x,…

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Q: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

Q: 191. The differential equation – tx = 0 dt2 can be shown to have basis solutions of the form a(t) =…

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Q: Let C′[a, b] be the set of all functions whose derivatives are continuous on [a, b]. Show that the…

A: Use the operator notation. where f is in C'[a,b]

Q: az az Use the chain rule to find and as at Z = In(3x + 5y), x = s sin(t), y = t cos(s) az az at

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Q: 2) Find the homogeneous linear ODE for which the given functions are Basis. -2x -2x , N, = Xe ", y3…

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Q: 2. Let V be the set of all the solutions of the differential equation y" + w?y = 0 in the form y =…

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

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Q: a. Show that the Bessel equation of order one-half 1 x²y" + xy' + (x² - - can be reduced to the…

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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: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: RIN Find the linearization L(x,y) of the function f(x,y)=e4x cos (3y) at the points (0,0) and 0₁-…

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Q: Solve these second order differential equations by applying the Laplace transform. (iii) y" + 4y =…

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Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = cos 4x

Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: 1. Let z = f(x, y) be defined by the given equation. Find the total differential of z at any point…

A: The solution of the problem is given in the next step.

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x -y . Use…

A: The given problem is to evaluate the integral using stokes theorem, we have to convert the line…

Q: azu(x, t) a?u(x, t) (-00 0) at2 ax2 u(x,0) = 4e-5|x| %3D (x,0)30 at

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Q: There are continuous functions p and q such that v1(t) = t lnt, 2(t) = ;? form a fundamental set of…

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Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: 1) Solve the Laplace equation for the function f(x,y,z) = (ax+by+cz)^n, where n is a given positive…

A: Part (1):   Given that f(x, y, z) = (ax + by + c z )n   Where, n is a positive integer and a, b, c…

Q: 56. By the transform method, solve 0 0, Ut = Urx + g (x,t), u (x, 0) = 0, 0 0. %3D

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Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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

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Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: Given X(u, v) = (a () cos u, a () sin u, ) 1-v² 1-02' 1+v2 2av 1+v2 COS u, a %3D (x(u, v), y(u, v),…

A: χ(u,v)=a1-v21+v2cos u,a1-v21+v2sin u, 2av1+v2 x(u,v)=a1-v21+v2cos uy(u,v)=a1-v21+v2sin…

Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: 2n Jnsi (x) = " J,(x) – J(4)

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Q: Represent f(x, y) (0<x < 4, 0 < y < 4) by a double Fourier series sin (). NTY f(x, y) = EEBmn Sin ()…

A: The given problem is to find the value of Bmn using double Fourier series with given f(x,y) series…

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

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Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

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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: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: a L, Vo, V (x) = Vo, For the finite well defined by its potential E<VO, apply the relevant boundary…

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given: f(x)=1+3x-5x3

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We have to find a linear differential operator that annihilates the given function.

Q: (1) (a) Show that the given line integral is independent of path. (b) Evaluate the integral by…

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Q: If U(x, y) = -e-Y sin x andf(z) = U(x, y) + iV(x, y) is analytic, then V(x, y) = %3D %3D -ey cos x…

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Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: Suppose I c [-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by 1, хEI x1(x)…

A: given suppose I⊂-1 , 1 is an interval . define the indicator function XI:-1 , 1→ℝ by XIx=1x∈I0x∉I…