(a) Calculate aw aw and using the following functions: - ди av х+2у — 42 2х — у + 3z w = f(x, y, z) %3D x = x(u, v) = e2u cos 3v y = y(u, v) = e2u sin 3v z = z(u, v) = e2u+v %3D

Q: c) Find i. y' for x4 + y = 17 If x = 3 and y = 3, calculate y'

A: Here is the solution of above problem.

Q: j Find y as a function of æ if a?y" – 9xy' + 25y = xº, (1) — 2, У(1) — -5. y =

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Q: Find the indicated value of the function f(x.y.z) = 3x - 5y? + 9z° - 6. f(9, – 3,1) f(9, - 3,1) = O

A: f(x,y,z)=3x-5y2+9z3-6f(9,-3,1)=3×9-5×((-3)2)+9(13)-6f(9,-3,1)=27-45+9-6f(9,-3,1)=36-51f(9,-3,1)=-15

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): =…

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Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: 3. Let w = f(z) = 5z² – 12z + 3 + 2i a. Determine u and v b. Calculate f (3 – 4i)

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Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

A:

Q: Q: Fin dx dfor the following functions: - 1- y = 2cot 2 xcos²(x³+1) V x cos (x+1) 2- y =

A: we have to find the derivative of the following y

Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: əz Find ( (). If (x, y, z)variables, and (2) a function in (x, y), and achieve the equation: 1 x-2 +…

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Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: dx 7. = cosx cos² t dt

A: 7). To solve the differential equation: dxdt=cosx cos2t Solution: Re-arranging the given…

Q: he equations æy² + 8xzcos(u) + ye" = 16 and x yz + xe" – 5u²v² = 15 are solved or u and v as…

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Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: The given equation is y=Aex+Bxex. We have to eliminate the arbitrary constants.

Q: 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a…

A: Given- The equation 80x'' + 1000x = 2500cosπvt6 To find- FInd the general solution to this…

Q: d²y Find and dx then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t2 –…

A: We have to find first and second derivative for the given parametric function.

Q: 1. y = Domain: Range: sec x 2. y = csc nx Domain: Range: 3. y =4 sec 3x 3 Domain: Range: 4. y = csc…

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Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. @ y = (c,+cx)e¯* + cze -2r + e*(c_,cosr + c zsinx)…

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Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

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Q: Find ∂z/∂t if z = sin(5x3-3y2), x = 2s2+t2, y = 2st3. Write in terms of the two independent…

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Q: Solve for the general solution of (D: - 1)y = sinx using variation of parameters y = cje¯* + ¢ze*…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.