Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

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Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: Evaluate [[ sin(y²)dydx where 2: 0<y<1, 0<x<y°. 0 x b) a-cos¢x)) (1 a) 1-cos(x) 1 - cos(1) c) 2 d)…

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Q: TC 16. Evaluate the definite integral cos2 (4t –) dt

A: 16. Now,

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: Write only the corresponding differential operator of y''+8y'-8y=0

A: The general form of linear ordinary differential equation of order n is yn+a1xyn-1+......+anxy=qx.…

Q: Find the differential dy of the given function. y = In√9-x² dy =

A: Given y=ln9-x2 Formula: ddx(ln u)=u'u where u is a function of x Now consider y=ln9-x2 The given…

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: Q,7 Evaluate the integral 1) L,x* dx 2) xVx+1 dx 3) f cos2xdx

A: we have to solve

Q: 1- d/dz [cosz] = -sin z

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Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

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Q: Find the differential dy of the given function. y = In√√/9-x² dy =

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Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: Show that a harmonic function u (x, y) satisfies the formal differential equa- = 0. azdz

A: Consider the provided question, Given, ux,y is harmonic function. We have to show that ∂2u∂z∂z¯=0.…

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: I need solution to this problem.

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Q: x²y' + 2xy = In x, У(1) 3D 2

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Q: In (6x) to x if y = sin (5e') dt.

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Q: The Soluton Curve for a differential equartion of the form an-y= 3n, passes through dy + passes. the…

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

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Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: ons z = sin y arn

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Q: 3) 6x + sin 5x + 10 cos x

A: Given function is fx=6x+sin5x+10cosx. We have to find the linear differential operator that…

Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.