The roots of the characteristic equation of (D2 – D+ Dy are A1 = 3 + 4i and A2 = 3 - 4i . 25 15 10 4 6 2 30 5 9 8 20 7 12 50 3.

Q: D Exponential Shifting Theorem 4 (D° + 4D°-3D - 18)4=24x°e-3× t 4D²-3D - 18)y = 24 x°e¯*

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Q: Write a function for the sinusoid shown. Ay 4 (0, 3) 3

A: The graph of kf(x) is the graph of f(x) vertically stretched (if k>1) /shrunk(if 0<k<1) by…

Q: dx + 2x dx = 2x²y² dy

A: dx+2xdyy=2x2y2dy dxdy+2xy=2x2y21x2dxdy+2yx=2y2.......1equlet 1x=v differentiate with respect to y…

Q: If u(x,y) =3x2y+2x2-y3-2y2, then u is harmonic %3D

A: A function u(x, y) is said to be harmonic if it satisfies the differential equation uxx+uyy=0. The…

Q: Use Green's Theorem to evaluate -15/4 O -218/3 O 19/2 [(6y - 9x) dy - (yx - x³) da where C' is shown…

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Q: Evaluate the complex function. Find u(x,y) and v(x,y) f (2) = e=" O e3ry sin(3x²y + y*) O e-3ry…

A: To use the following problem we use the following result Z = x+iy  ez = e(x+iy) = ex( cosy +i siny)…

Q: 5. Find dy: dx (a) y = cas (21x² + 6x + 2) 4 (b) y = cas² (21x² + 6x + 2)

A: The given functions

Q: 1. Evaluate 2dw а. 5-4w-2w2

A: a) Evaluate: ∫2dw5-4w-2w2

Q: . du/dv = (u - v)2 - 2(u -v) - 2

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Q: Show that if an = 5n3 - 14n2 + 7n - 3, then an = Θ(n3).

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Q: Show

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Q: Question 2 12x +1 dxp. (2x- 1)2 (3x + 2)² Evaluate:

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Q: Determine for which values of m the function (x) = xm is a solution to the given equation. d²y dy -…

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Q: 2 a. (1+5 ln x)³ dx fa+ b. (1+3 tan x)² sec? x dx 2x + 5 dx Vr – 3 2x3 – 5x? + 9x – 4 C. - d. dx x²…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: 24 + 16 = 0 e22-2z-3 = 0 iz = (-i)(-i)

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Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Question 18 Find the solution. (D5 - D³ly = 0 A y = (c,+c)xe*+czx+c,e"+cge¯ B ) y = (c,…

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Q: If p dP > dx which of the following is equivalent to ~ +(²+²)(-+) " ( + + P ) ( = = 2 + P }) Inx+P…

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Q: 7 Integrate: 2 -dr ² – 4x + 13 + C

A: let I=∫7x2-4x+13 make the complete square of denominator i.e. (x-2)2+9. using substitution method…

Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

Q: What is the most appropriate substitution equation in order to solve the equation…

A: The given differential equation is -  (x+2y-1)dx+3(x+2y)dy=0 Rewriting the above equation as  -…