The complementary function (CF) of the differential equation y" – 2y' + 2 y = 0 is a) CF=e"[c, cos .x +c, sinx] b) CF=[c, cos x+c,sin x| c) CF=e*[c, cosx+c, sin x] d) None of these C O d O b a

Q: A1. The differential equation of the function y = ax? + b where 'a' and 'b' are constant is: a) y' =…

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Q: The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: The solution of the differential equation (1 + x²). A tan + k B tan-(x) + k C cot-' () + k D…

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Q: The standard form of the following linear differential equation sec(x) y' + csc(x) y = 1 is: O…

A: Option A

Q: Differentiate y = sin(3x + 4y) cos(3x+4y) 1+ 4 cos(3x+4y) з cos(3x+4y) 1+4 cos(3x+4y) cos(3x+4y) a.…

A: y=sin3x+4y

Q: dy = [cotytant cosx dx cosy A siny?= sin2xln(csinx) (B siny= sinxln(csinx) siny= sin2yln(csin?x) D…

A: There is something missing in the given answer list.So The solution with correct answer is given as…

Q: The complementary function(C.F.) of the differential equation (D2 + 6D+ 18)y= z is_

A: In this question, we have find the complementary function for the differential equation.

Q: The differential equation 3zy" – 2y + 7y = tan x is normal on any open interval not containing = 0.

A: The main objective is to determine the given statement is true or false.

Q: 2. Evaluate whether the following initial values is true in the function: y = 4cos-+ e-2x 2.a) 2.b)…

A: Given , y=4 cosx2+e-2x

Q: What is the order of the differential equation M – R()* = (#)' ds dt? dS sin St? dr2 dr

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Q: (x - v)y" - v =tanx is second order Ilinear differential equation. Select one: O True O False

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Q: Consider the differential equation 4y' = 3y+ 2x/y Which of the following is the linear form of this…

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Q: 2 Find the second derivative of y = 1½ cos² x. Oy" = COS x 2 y" = COS X sin² x cos² - Oy" = sin² x =…

A: Q.Consider, y=21​cos2x Differentiate with respect to x. y′=21​dxd​(cos2x) Use formula:…

Q: Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C,…

A: To find  The general solution of the given differential equation.

Q: The differential equation (2 tan(2x) - 2 sin(2x) sin(y))dx + (cos(2x) cos(y Has solutions of form…

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Q: b) y' = =+ cos) COS Hint: use the change o variable u =

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Q: Hint: Use method of undetermined coefficient Solve using the differential operator D=d/dx y" - 2y' +…

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Q: Q16: Is the differential equation (cos x + In y) dx + +e) dy = 0 exact?

A: To check the given differential is exact or not.

Q: Check whether the functions which satisfy the following differential equation are linearly…

A: Given differential equation x3d3ydx3+31-αx2d2ydx2+3α2+β2-3β+1xdydx-αα2+β2y=0 Given differential…

Q: find differential equation of the following equation 1) y' = y-x y+x

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: b) Form the differential equation from the function x = Acos(nt + a). e) Given that y = eax sin bx,…

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Q: Transform into first order linear form the differential equation (1 cos z) y' sinz (sin z + sin…

A: The given differential equation is                                  (1+cos x)y'=sin x (sin x+sin x…

Q: Evaluate the given differential equation y' tan x sin 2y = sin²x + cos²y A. sinx (sin'x + cos°x) = C…

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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.