Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1- y3 = 3x (c) y'- Iny = 0 (d) + 2 + = 2sin(x) %3D

Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: Divide P(x)=8x-4x+2x-1 by D(x)=2x-1 Find the quotient, Q(x), and the remainder, R(x) Write an…

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Q: Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are…

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Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: VT-x- 5 | f(x) = 6.

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Q: Find the point on the graph of f(x)=4−x2 that is closest to the point (0,1).

A: To find the point on the graph of fx=4-x2 that is closest to the point (0,1)

Q: Find an equation for the linear function which has f (0.5) = 0.8 and f (0.8) = -0.3. f (x) =

A: We have to find the linear function where, f0.5=0.8 and f0.8=-0.3 We know linear function form,…

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.