Which of the following is a differential operator that annihilates the function y= 5x* + Sx2 +6r +5 cos(4x) +4e/2. 0.D(2D-1)(D² +8) O None of these o D°(D-1)(D² +4) 0D (2D+1)(D²-16) o.D°(2D-1)(D²+16)

Q: Which of the following differential forms are exact? (y² – t²) dt + (2ty – y) dy O ye' dt – e' dy O…

A: To find  Which of the given differential equations are exact.

Q: 31²+1 dt = Compute:

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: f (t) = t(e-2t + cos at)

A:

Q: dx dy y²+x² 3x²y+y³+2xy

A:

Q: 18 through 21, find an integrating factor and solve In each of Problems the given equation. 18.…

A: Given Data: Let us consider the given equation is: y+2xy-e-2yy'=0.

Q: Write only the corresponding differential operator of y''+8y'-8y=0

A: The general form of linear ordinary differential equation of order n is yn+a1xyn-1+......+anxy=qx.…

Q: - x dy = 0

A:

Q: S e-t cos(e-t)dt 3.

A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: eft R3= f(1) + f(2) + f(3) = 1² +2²+3² 7/14/ 6. Find the derivative of x² + xy + y² = 27 d 2x (x² +…

A: Find rate of change

Q: 3x (y? + y + cos4y)dydx 3.

A:

Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –…

A:

Q: dy Q1: Solve the DE x3 dx3 +x = x Inx cos(2lnx) by using inverse dx operator method.

A: Given differential equation is .....1 Its solution is given by yx=C.S + P.I ; where C.S is…

Q: Beta Function dx 3) Evaluare ta) "(4 – u)". du, (h) Ans. (a) 12л. (h) п 3x -x

A:

Q: (a) Explain test whether the DE (cos y) dx + (y² - x sin y)dy = 0 has an integral function, say p.…

A: Part a

Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: State True or False, no justification needed. (a) The functions f₁ (t) = t and f2(t) = e²t are…

A:

Q: dy dx cos(x + y) = 3x Find dy dx dy dx dy dx dy dx = = -3 csc (x + y) - 1 = -3 cos(x + y) - 1 = −3…

A: we need to find out the derivative.

Q: -2 | (t2 + 3) cos(5t)dt 0.

A:

Q: Find the general solution of (d²s)/(dt²) + 2(ds/dt) + 5s = 0. OA.y = C₁e(t) cos2t + C2 e(t) sin3t…

A: Let's solve given diffrential equation.

Q: Show that (i) | te 3 sint dt 50 -3t %3D

A:

Q: (a) Explain how we can test whether the DE (cos y) dx + (y² - x sin y)dy = 0 has an integral…

A:

Q: 1. F = cos y i+ xyj + yk, A B C D E F О н A. i+j+(y-siny)k B. i+ (siny - y)k C. j (2y-siny)k D. 3i -…

A:

Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

A:

Q: (xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

A: As two questions are given , I will solve only the first one. Given : f(t)=3+e4t-te-2t+e5tcos3t+6…

Q: [t5 ] = ? %3D 120 24 s6 O A D QI L[(t+ 1)?e] = ? 24 120 s5 Oc B s2 + 1 s2-1 L [sin? (t) + cos?(t)] =…

A: Given 1 Lt52 Lt+12et3 Lsin2t+cos2t

Q: 1. Find a differential operator that annihilates the function xe2 ( cos 3x + 3).

A: Given problem is :

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

A:

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: Find the Annihilator of the given function(s) f(x) = cos(2x) + 4sin(3x) a. (D²+3)² b. C. d. D² -3D+4…

A: answer is b

Q: a) Determinethe Fourier Transform Y(w) of y(t) from the differential equation (2) above. b) What…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: 2. f(1) =t cos 81 +2

A:

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.