Which form should you use to determine a particular solution of the following differential equation? y(7) – 4y(®) – 4y(5) + 56y(4) – 156y(3) + 224y" – 176y' + 64y = e* cos(x) – 3e2x + xe -4x (1) yp = (A1x? + A2x)e¬4x + A3e²x + A4xe* cos(x) + Aşxe* sin(x) (2) yp = A,xe2x + (A2x + A3)e4x + A4e* cos(x) + A,e*cos(x) (3) yp = A1xe* cos(x) + A,xe* sin(x) + A3x²e2x + (A4x+ A5)e-4x (4) yp = A1x²e* cos(x) + A2x²e* sin(x) + A3x²e²x + (A4x² + A,x)e¬4x (5) yp = A1x'e²x + (A2x + A3)e¯ -4x + A4e* cos(x) + Age* sin(x) (6) yp = A1e2x + A2xe* cos(x) + A3xe* sin(x) + (A4x+ A5)e4

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A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

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A: Explanation of the answer is as follows

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A: given  y=Aex+Bxex we have to form the differential equation .

Q: State the order and degree of each Differential Equation

A: We will find out the required values.

Q: xy' =yelx-x

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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.