Consider the function T = xe3x+y? dy 5 and dt where x = Vt + 1, and when t O we have y -2. dT when t: dt = 0. Use the Calclll chain rule to find ||

Q: Find the Laplace transformation of the following: 1) (2t² – 1)2 2) cos³t 3) sinh³t Hint: sin CoS

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Q: Evaluate y' of the given functions: 1. y = (x² – 2)(x + 3)

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Q: Find d2y/dx2 as a function of t if x = t - t2 and y = t - t3

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Find the Atend and matnix gF

A: Given a T be a linear transformation and Tx,y=x+y,y−x We have to find the standard matrix of T Let…

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

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Q: verify that (A + B)T = AT + BT

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Q: Find dydx for the function y=3x.

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Q: F = (2+-1) dt

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Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Find y as a function of t if 16y" – 72y' + 72y= 0, and y(4) = 9, y' (4) = 8. y =

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