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

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Q: 5 Find xy dydx. 4

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Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

Q: 5 Find xy dydx.

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A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

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Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

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Q: 1-E-, find x, y from エ+y 4. 3 3.

A: given two matrices are equal. that means, Both matrices have same order, and the corresponding…

Q: /4 - x2 the integral | dx, becomes

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Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: If =4xy, find x and y components of the velocity at (1,4)  and (4,4). Calculate the discharge…

A: Given that, ϕx,y=4xy    ...1. Let the points be, x1,y1=1,4 and x2,y2=4,4. Consider the velocity…

Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

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Q: When two particles start at the origin with velocities v(t)=cost and u(t)=sin2t, how many times in…

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Q: Suppose that an initially full hemispherical water tank of radius 1 m has its flat side as its…

A: Given:

Q: 2. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

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Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

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Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Find y' where y = (tan(18z² +5)) / 18z3 +14 Answer: 54z2 O v' = sec2 (36z) /1823 + 14 + tan(182² +…

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Q: 4. You will need to use L'Hopitals Rule in this one Sxe-* dx

A: This is a improper integral problem

Q: Express he equation n" = 4y in poar corinaes.

A: Given equation x2=4y

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Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: 4. Find derivatice y 4=In (x 3-4x²+1)

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Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

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Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A: