a. Z1 Z2 = r1 r2 [cos(0, + 02) + j sin(0, + 02)] %3D Z1 =" [cos(0, - 02) +j sin(01 – 02)] b. | | Z2 r2

Q: The general solution of (D2-2D+1)y=2sin x A y= ce*+c>xe* + sinx B y=ce*+c2xe* + sinx+cos x…

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Q: (D² - 4D + 5)y = e*; y a. y= e²*(C,cos2x + C,sin2x) – –e 10 b. y e2*(C,cosx + C,sinx) +e 10 C. y =…

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Q: y" – 9y = t° – t e + sin(3t)

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Q: z 3e*3S,y 3z2 + sin(z)s G dx

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Q: 12 A A10. If B then the values of A& B =. %3D (x-2) (x+4) x-2x+4 A 2, – 2 b) -2, – 2 c) 2, 2 d) -2,…

A: Since you have posted multiple questions we will solve the first question for you. If you want any…

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: z = sin(6x) sin(5y) az az dy II

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: d 1+ sin² (2)| dz

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Q: (D² – 2D - 3)y = 2sin x a. , =cosx -sinx =-cosx -sinx c. = -cosx +sinx COSX 1 b. yp С. Ур 21 COSX d.…

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Q: [9x cos(3x + 8) dx = Select one: a. 3x sin(3x+8)-cos(3x+8) O b. 3x sin(3x+8)+cos(3x+8) C. d. + C + C…

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Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: (D³ - 3D2 + 9D + 13)y = 0

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Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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Q: Yp = A1 cos V2t + A2 sin V 2t Which of the following is Yp'? sin v2t A1 V2 Cos /2t A2 V2 O V2A1 sin…

A: Please see the explanation below

Q: If x³y" + xy' +(x? -y=D0 x>0 ,y,=x sinx , and y3V,v. Which of the following 3 equations satisfied by…

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Q: d (c) (cos(2²) + In(3 – 2æ)) dx

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Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: (c) /* sin 6. 3 sin Od0 (0)

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Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

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Q: Find the expression for dy dx dy dx dy 2xcos(x²-y²) - 1 2ycos(x2-y2)+1 dx The answer cannot be found…

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Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

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Q: f (t) =-e" sin (21 +7)

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Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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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.