3. Given that g(r, y) = x² + y? subject to ry = 1, show that g(x, y) has no maxi- mum points. (Hint: use the Lagrange method)

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: Use Euler's Method with step size h=0.1 to approximate y(1.2), where y(x) satisfies the following…

A: Given initial value problem is  y'=3x+y y1=31

Q: Given a level suface 4x2y2 + 5xy = 4 with y = y(x). Find! dy at the point (3, 2). Give your answer…

A: A detailed solution is given below

Q: L'équation 423 = In (e4% + 2ay) définit implicitement z comme fonction de x et de y au voisinage du…

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Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. y' =…

A: To solve the given differential equation by Runge kutta Method of order 4 first we fill find the…

Q: 4) Solve the followingIVPusing LaplaceTransform. y′′−6y′+15y=2sin(3t)    ,y(0)=−1,y′(0)=−4

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Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.4) using the…

A: Let y'=f(x, y). Runge-kutta method of  fourth order also known as RK-4 method uses the formulas…

Q: pプ PG2-2(6x)さ子エ theorem over the elosed hemispher defined bY Zz J25-x²_y?

A: Given that F→=x2+yi^-zyj^+z2k^ and z=25-x2-y2

Q: Modify the method of Cauchy-Euler DEQ to find a general solution to the following DEQ for t > 2 (t –…

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Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

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Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: Consider I = , f(x)dx. The approximation of I using composite trapezoidal rule with 3 subintervals…

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Q: 8.9. The volume V of the liquid contained in the spherical tank of radius r is related with the…

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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: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Solve the following initial and boundary problems Luz + (4x – 1) uy = 0 (a) и (0, у) — Im y. { %3D

A: We have to solve the given initial and boundary problems.…

Q: Given Y Z tangent to OJ at point Y, and mzWYZ = 104°, what is m WXY %3D Y W m W XY

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Q: 41. In each part, confirm that the stated formula is the local linear approximation at (0, 0). 2x +…

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Q: Using the Euler's method with step size h = 0.2, approximate y(0.4) if %3D y = y? – 2.2, y(0) = 1.

A: The solution is given by using the Euler's method as follows

Q: 4)Solve the followingIVPusing LaplaceTransform y′′−10y′+9y=5t,y(0)=−1, y′(0)=2

A: The differential equation is given as y''-10y'+9y=5t Apply Laplace on both sides, we get…

Q: dy 3 4-1+2у, dt (0) = 1

A: Given dydt=4-t+2y   ; y(0)=1  with h=0.1

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

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Q: If yV2) is a fundamental set of solutions for the DE: t'y"-3y' +costy3D0 and if W(v,V2)(1) =2, then…

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Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

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: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: For x,y,z > 0, use the Lagrange Multiplier Method to find the minimum value of 1 1 1 + + x y Subject…

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Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: ürkçe: f(x, y) = 4 + x° + y° – 9xy fonksiyonunun yerel ninimum değerini bulunuz.

A: Please refer to the image below

Q: The indicated Turi Is a solution of th1e given d merentiai equation. Ose iula (5) Tn Section 4.2…

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Q: Solve the boundary-value problem by method of separation of variables: du Su +3 Sy = 2u, given u (x,…

A: A

Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: Use methed of Cardinates to Solve PDE du t 37gu = o (32² +81y -3y) for V 64) E R for Y te B with the…

A: We will use the approach of the method you mentioned.

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.