T: P2 P2, .2 T(ax2 + bx + c) = ax² + bx +c B = {1, 1 – x, (1 - x)²} B' = {1, x , x²} v = x² – 3x +3 -

Q: y" + 2y' – 3y = 0

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Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: Integrate counterclockwise around C. (Show the det に+1 20. ‚ C: |z − 1| = 3 - ²-iz + 2

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Q: b) Golve: 4x°y*+4x°4- sx y' + 24= 60x?+8x +1 on Co,00) (2) vsing the Method of Uaniation of…

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Q: Q-23 (aT trajectories of the families of y? = 2ax, where a Find the orthogonal being a parameter.

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Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: Find L(x). 2y -a = 3t y+z' = 3e z (0) = y (0) = 0 = (x) T0 (s+1)(s–2)(s²+1) OL(z) = 3s2 3(s-1) %3D…

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Q: 7. Evaluatexyddx+e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

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Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

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Q: Vx2 +1 – Vx² – 1 y = Vx² +1+ vx² – 1 2.x3 dy = 2x - d.x - - show that Vx4 – 1 -

A: Given: y=x2+1-x2-1x2+1+x2-1      ......(1) To Prove:  dydx=2x-2x3x4-1      ......(2)

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

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Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

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

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Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: s lineax diggerential Solve nonhomogene ous equation using propesty of diggerential operator I…

A: Auxiliary equation of given ODE is  m3-2m-1=0m2-m-1m+1=0 So we have Complementary solution is…

Q: The solution of y" = 8(t – 1) – 6(t – 3), y(0) = y'(0) = 0 is y(t) = %3D (A) (t- 3)[u(t - 1) - u(t-…

A: Given y''=δt-1-δt-3, y0=y'0=0

Q: = S, (x²(t) + x²(t))dt %3D x(0) = 1, x(1) = free %3D

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Q: y" – 2y – 2y = 0

A: Given:      y''-2y'-2y=0       -2yx-2ddxyx+d2dx2yx=0 The differential equation has the form:…

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: From the given information the given curves from which the volume is to be generated are:

Q: 8. Find the orthogonal trajectories of y = cx CX

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Q: 6y" – 5y' + y = 0, y(0) = 4, y'(0) = 0

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Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: 1 1 J(A) = ,T AX 2 i=1 j=1 =;(x1A11x1 + X1A12×2 + X2A21X1 + x2Az (A - yariable, X-parameter)

A: Given,      J(A)=12XTAx      =12∑i=12∑j=12xiAijxj      =12x1A11x1+x1A12x2+x2A21x1+x2A22x2where A…

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

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Q: xy" – 2y' +=y = 7x5 Given that y, = x² and y2 = x are 2 Linearly independent soluti homogenous…

A: Introduction: The formula for the particular solution by variation of the parameter is given by,…

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: (x, y) - arty! - b where x is the amount of money expended on labor, y is the amount expended on…

A: Solution is below

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: Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…