Solve bollowing 4ntial value paob lem the 2dy +30y=4(u+2)²lnac? ; x20, yla)=0 1)%3D0 %3D dx

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

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Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 10 In(x) dx,n = 6

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Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

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Q: 5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y,…

A: We have to solve given problem:

Q: To evaluate fx (cosx²)e** dx, use integration by parts. What is the best choice for u and du? u = x…

A: Integral by parts.

Q: The longest interval in which the 1.V.P y" +(tanx)y- xy = x, y(1) = 3, y'(1) =0 surlay has a…

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Q: Compute yarctar y? = 1 – 1+ y? ctan(y)dy. Hint: Note that 1+ y? fractan(g)dy- +C

A: we have to comloute the integral ∫ y tan-1 (y) dy we solve this integral by integration by parts…

Q: X > U (M-, M+) M, Xca) 3. X(2) rimators: 2 1x

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: d?x +x = secy %3D dy2

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

Q: (h) Ã(x, y, z) = yɛ, – xë, (i) Ã(x, y, z) = ex + ey x² + y?

A: For the conversion between cylindrical and Cartesian coordinates,  the z-coordinate is the same in…

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

Q: 2n P(X = n) = c, n= 0,1, 2, .. n! a) c sabitinin değerini bulunuz. b) P(2 s x < 3) =?

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Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

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Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: ® Use Craumoy's rule to solre fhe following linear syslems: rele to solve al fxy=0 8? S x+2y-2 = 0…

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Q: Evaluate the integrand S(2 + 5x)e dx using IBP. A. 5xe – 39e* + c B. 15xe – 39e* +c c. 15xe* – 9e*…

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Q: Evaluate 3xz dV where E = {(r, y, z) | 2 < ¤ < 4, x < y < 2x, 0 < z < x + 2y}

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Q: Euler's difFQ 3. (y()) =VZ Eq cal g'ral-2y cx ) =x (y (x )

A: Given differential  equation:-    y' - 2y = xy3        y(1)=2√2

Q: Check for homogeneity and obtain the general solution. (Let y=vx and 2C=C) dy x-y dx x+y

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Q: 1 Px1x2(w1, W2) = (1– j2w1)(1 – j2w2) | 13 The joint moment m20 is equal to

A: # joint moment m20=E(x1^2)=-8

Q: Exercises 41 and 42, evaluate (y – x) dx + (2x + 5y) dy. 41. C: line segments from (0, 0) to (2, –…

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Q: 2: Salve the fallowing differnilial eguitins Yx) =4 Hint: Riccati D-Eymtim.

A: Given equation is, dydx=12xy2-1xy-4x One solution is Y(x)=4.

Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: The longest interval in which the 1.V.P y"+(tanx)y-xy = x, y(1) = 3, y'(1) =0 surlay has a solution…

A: Given differential equation is. y''+tanxy'-xy=x The initial condition as, y1=3,  y'1=0 On comparing…

Q: Solve using horizantal S,ļide EX g. Evaluabt.fx.d. wha..ia.the..rsgem.in.the first quadrant.bounded.…

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Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: The longest interval in which the 1.V.P y"+(tanx)y- xy = x, y(1) = 3, y'(1) = 0 surlay has a…

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Q: (p;-q,)? 2. Prove that KLD(p||q) = J6 t Eisisn pitt(ai-p) dt. %3D

A: Given: To show the given statement as follows: KLD (p|| q) = ∫01t ∑1 ≤i ≤ n pi-qi2pi+i( qi- pi) dt

Q: 4) answer: Check for Linear Independence 2x fi - e e; f2= i fs e* Say sa'y dx" 4 dy dx dx get the…

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Q: dy 3. da + y = 2xy?e"

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Q: Solve Fyy + 3 Fry + 2 Fx = -3 x, F (x,0) = x, dy F(x,0) = 0. ху XX F(x, y) =

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Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: 8 Exercise.3 Evaluate y* Va? – y² dy [+hint: assume y² = a?x], [M Check answer: %3D 32

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Q: Solve the fello wing differntial equation by ieg Lapla ce trans frmation dy +2y=0, dt , where…

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Q: Assume butterflies' populace caleulated that aftes W months, in lo06 is as f lW) = 12W + Los…

A: Given f(w) = 12w + cos(16w) +n * 100

Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

A: follow next step

Q: Given the joint pdf of X and Y is fxy(x, y) Find P(X>Y). = -{abe abe-(ax+by) x>0, y>0 otherwise

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Q: f(L,K) + x [loo-PeL-Pak] max dQ

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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.