Which of the following is the correct form of the solution to the non- dy homogeneous equation for 4y = 8e* – 3 sin(2t) – 7 cos(2t) dt y = a sin(-4t) +b cos(-4t) y = a sin(2t) + b cos(2t) y = aet + b cos(2t) y = aet +bsin(2t) y = aet + bsin(2t)+ ccos(2t)

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: Find az/ax and dz/dy. xyz + cos(xy) - 2y sin(x) + z² = 3 Find az/ax and dz/dy. exz ZX y

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Q: y" +2y' = 3+ 4 sin(2t)

A:

Q: SO FO %A4 Find dy/dt. y cos(W10t +1 -sin(ot +11 5. sin(~10t + 11) II + 301 +101 sin(~10t + 11) II +…

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Q: Assume that the equation system x2 - xy +In z = 1 - In(2) exy-yz + 2z² = 3 13/1/2 dx 2=1/1/21- dz…

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Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: explain in full detial

A: Step 1: Step 2: Step 3: Step 4:

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.