If we use the variation of parameters for the equation y"+ y = tan(t) by solving uj cos(t) + ug sin(t) = 0 - uj sin(t) + uz cos(t) = tan(t) what do we get for u1? sin(t) - In sec(t) + tan(t) O u1 -cos(t) = In O u1 sin(t) sin (t) cos(t)

Q: b) Differentiate (i) (i) the following functions clearly showing your working y = cos (4x4) y =…

A: Let us differentiate the functions with respect to x in the next steps.

Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: 6) y=-sin (3x) - 1

A: 6. The given function y=-sin3πx-1. We have to sketch the graph of the function and find its domain…

Q: Find sin (x) if sec (x) sin (x) A = B = B = 26 24' where tan > 0. Put your answer in reduced form.

A:

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: Find y' where y where y = 10 sin-1 (cos (21 z)) - tan C BARANG (18 r)

A: Given: Now,             y'=10arcsincos21x-arctan18x'     =10arcsincos21x' -arctan18x'…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 2) y = sin(3x²ex)

A: Find the derivative

Q: a. GRAPH one correct (and correctly labeled) cycle of the given b. State the Domain and Range of the…

A: A function y=tanπx3. To Find: a) Sketch the graph of the function. b) Domain and range.

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.