2. Solve the following Cauchy problem: xyu, + yu, + yu = y – x with 1 u = -- y = x². on

Q: 1. /v + x = z, for v Solve

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Q: 3) Find x if IS = x and IQ = 2x – 5 S. R

A: given,     IS=x , IQ=2x-5

Q: 15. z+i · (z − 1 − i)³(z − i) JR-1 dz

A:

Q: Evaluate I 5/2 U (4-u) du · Su² 3/2

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Q: solve For B, and B₂ 0 = -22 0 = = 2 2 i=1 Xii lyi - (B₁ Xii + B₂ Xiz)) x ₁₂ (y₁ - (B₁ Xi₁ + B₂ Xiz))

A: Given system of equations0=−2∑i=1nXi1(yi−(β1Xi1+β2Xi2))0=−2∑i=1nXi2(yi−(β1Xi1+β2Xi2))Which can be…

Q: Q1) L-¹ (²-1) = a) cosht -1 Q2) The general solution of y"" + 2y" -y'-2y = 0, is: 2x a) y(x) = c₁e²x…

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Q: x²j + 3xỹ + 5y = (x) uj 2*.

A:

Q: 3 1 = (-1 5 3 and b 0 3/ 2 '3' Find A-b if A 2 %3D 3

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Q: 6. Given r + y° = 1, find y"

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Q: 7-9. Write the polynomial in factored form and then in standard form (multiply it out) with the…

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Q: 1. Find 2(3z + 4)² dz.

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Q: 3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

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Q: Solve for u. u/2 + 3u/4 = u/8

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Q: 12 +3t-4 and 3t2-3 9.) Suppose that x = 3x 10

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Q: What are the solutions of the equation 2sin(4x)=1 on the interval [0,n)?

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Q: 3 y`dy 3 (4 -у?): 2

A:

Q: For the model y = Bo + B₁X₁ + B₂X₂ + ε, instead of coding the indicator for X₂ as (1,0), the analyst…

A: Given model is y=β0+β1X1+β2X2+ε Previous indicator of X2 is 1,0. New indicator of X2 is 0,1.

Q: EX:- Select Analog to Convert 2X + y - 3Z - 2u = 0 __(1) X + 2y +Z+ u = 0. (2)

A: We are given a linear system and we have to convert it into analog matrix form.

Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: 8. Find y'ifys34-7x+2)+4%-2

A: Differentiation

Q: 9) If y = 3x +x² - 5 and z = x2 - 12, find 2(y +z).

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Q: 6. (x – 1

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Q: 10. Find x and y, given that (x² + y²,4) = (25, x).

A: When the Cartesian product is performed between two sets, as a result, an ordered pair is obtained.…

Q: 1. + (х+2)(х-2) x-2 2.

A:

Q: How many reams of bond paper can you buy for (x* + x3 - 7x2 - x + 6) pesos if one ream costs (x + 3)…

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Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

Q: Find yp for y" + 5y' + 4y = -2x + 3 1- O Option 1 XIN 2 +8+ C

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Q: 1. Find y if y =x In(4x+1).

A: Use the product rule of differentiation.

Q: Trigo Substitution

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Q: 1. Given the algebraic function x² xy + y² = 3

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Q: 4. Simplify: (i – 1)² – (-i – 1)² + i*, i = v-1

A: Given: i-12--i-12+i4 ,  i=-1

Q: If z = 3x² + y² and (x, y) changes from (1, 1) to (1.05, 0.9), compare the values of Az and dz. dz =…

A: The objective of the question is to compare the values of Δz and dz for the given function z = 3x² +…

Q: If i = xi+yi+zk then grad (r") is equal to

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Q: 2- S5olve X" = LX given u =1

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Q: -Suppose-Z₁ =3+2i, z₂ =4−5i . Calculate-|6z₁ - 9z₂|

A: AnswerGiven complex numbers z1=3+2i and  z2​=4−5i, we want to calculate the modulus of the…