Consider the D.E. y(4) + 4y" = 1 – cos(2æ). Then a suitable form of the particular solution can be written as y,(x) = (A) Ar +¤[B cos(2z) + C sin(2x)] (B) Ar² +¤[B cos(2z) + C sin(2x)]| (C) Aæ² + B cos(2z) + C sin(2z) (D) Ar+ B cos(2z) + C sin(2x) (E) None

Q: If sin(x + y) = -sin x + = sinx 2 OT 2 K|M 3 k|4 24 6 -cos x, what is the value of y? 2

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Q: b) 6(sin x)² + cos 2x + 1 = 0 [0,2π] I

A: Solution6 sin2x+cos 2x+1=0we know cos 2 x= 1-2 sin2xput this value in the given equation,6 sin2 x+…

Q: 2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂(t)…

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Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: 3. Simplify x(t) = 3 cos(27200t + + sin(27200t + to the form x(t) = a cos(27200t + 0) where a and 0…

A: To convert an expression of the form Acosx ±Bsinxmultiply and divide by A2+B2=A2+B2AcosxA2+B2…

Q: How long will it take to drive 700 km at 100 km per hour, if you take a 1-hour break after every 5…

A: We have to find time taken to drive 700km using given data. We will use formulaes,…

Q: Evaluate: Jx?cos(2x)dx 2x2sin(2x) + 2xcos(2x) + sin(2x) A + C 4 2x2sin(2x) – 2xcos(2x) + sin(2x) В +…

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Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: | 12 csc² (62) cot(6) dæ = 12 csc (6x) cot(6x) dx : (Use Substitution Method) %3D 12 12 +C 12 sin?…

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Q: What is the solution of the following equation: y(t) sin(t – t) dt = t Select one: a.…

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Q: If z = 1+ 2i and w 3+ 4i, express in rectangular form 5 cos [Arg (2²)] + 5i sin[Arg w]

A: The square of a complex number z is the product of z with itself. Multiply 1+2i by 1+2i to obtain…

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: 6. Use Pg4 or P¢-a (you have to pick the right one!) to transform the following function as a linear…

A: Given: B=1, cost, cos2t, cos3t, cos4t, cos5t, cos6tC=1, cost, cos2t, cos3t, cos4t, cos5t, cos6t

Q: Determine the general solution to (D² + 4)(f) = sin(2x) satisfying the initial condition: f (0) = 0,…

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Q: 3. Solve the equation: (Dª – 1) y = 0

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Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: Consider the D.E. y+4y" 1- cos(2r). Then a suitable form of the particular solution can be written…

A: A linear non-homogeneous ordinary differential equation with constant coefficient has the form…

Q: 3) fe-2x sin 2x dx 4) J√1 + cos 4x dx

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Q: 1 L- s3 + 4s (A) (1 – cos 2t] (B) (1 – cos 2t] (C) (1 – sin 2t] (D) [4 – cos 2t] (E) [1+ cos 2t] Ο Α…

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Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: Find the solution for L{e-3t(cos(5t) – sin(5t)}. Find the solution for L-1{E + 10}.

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Q: Find all values of a for which the equation : 10х — 2л2 — а - cos (2x + a) = x² – 8x – C cos 3 has a…

A: Given equation is  cos10x-2x2-a3-cos2x+a=x2-8x-a               (i) First, let us solve the following…

Q: Determine fe when f(x, y) = 2x - y x + 2y

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Q: 2. Solve the following DEs and PDES: (a) I = 3r +1 = 3r +1 (c) G.v) = Ar + B df(z) (b) f(z.y) (d)…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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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: What is an equation for the cosine graph shown below? -135 -90 -45 -11 -10 +9 8/ -7 -6 -5 3 2 1 45…

A: Given query is to find the cosine equation of the function.

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.