b) (i) Show that dz is a constant independent of z, and R. { Hint : z= Z, + Re"} 1 +- 2z-4 2 -z 3 (ii) Hence, evaluate dz. k--10

Q: 8y'' - 12y' + 5y = 6 cos t

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A: 34) Solve the integration:

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

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A: We can answer all the three question as below.

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

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Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

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A: Differentiation wrt x

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

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: A homogenous linear differential equation with variable coefficients given by,…

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A: Given, y'=t-2y y(2)=3

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Q: xy ,show that: x- y If z = = 0

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Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

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Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

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Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: s zy dydz こミ0

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Q: 2. u(x)= secx+à So u(1)dt.

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A:

Q: =y一;-T十;-一

A: Draw the family of these one parameter DE's of bifurcation.    Further, to solve these.

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

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A: As per bartleby guideline for more than one question asked only first is to be answered please…

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A: Since you are asking part (c). We are answering only the (c) part for you.…