Which of the following functions is a solution of da 12x 8y | dt dy 16х - 4у dt O a. x(t) = e2t cos(8t) – e2t sin(8t) |3| -4t O b. r(t) = e 4 cos(8t) – e t sin(8t) -4t O c. r(t) = et cos(8t) – et sin(8t) COS O d. a(t) = e 4 cos(8t) + e " sin(8t) O e. a(t) = e" cos(4t) + e4 sin(4t) COS

Q: Solve the following DE by using separation of variables or method used in solving exact DE

A:

Q: Q11) The general solution of y" - 4y' +9y = 0, is: a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)…

A: Solution :-

Q: Find the solution x (t) of the IVP given as a" + 4x' + 13x = f (t) x (0) = 0 and x' (0) = 0 -37 A) x…

A:

Q: d² dx dx 3. di² +2 +5x = sin 21, given that when t = 0, x = 3 and dt dt 53 [ 55 Ans. e 17 cos 2t + -…

A:

Q: Q1/ Determine a complete solution of the following system of the WARITH AL-AN differential solution…

A:

Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: a. Prove that the O.D.E: (2y+2x-5)dx+(6y+2x-1)dy=0 is exact and solve it.

A: First we will check if this equation is exact.

Q: Q.2// Solve the following pair of simultaneous differential equations Using Laplace Transform: dy dt…

A: By Laplace Transformation we know that, 1. ℒ(sinat) =a2s2+a2 2. ℒ(eat) =1s-a

Q: is Fill in the following blanks: (( = 3x² cos 5x), 5) By using the method of undetermined…

A: We need to complete the given fill in the blanks.

Q: Consider the D.E. y(4) +4y" 1- cos(2x). Then a suitable form of the particular solution can be…

A:

Q: Which one of the following differential forms is exact? O a. 2x²ydr-4xy'dy+8z°xdz O b. 2cosx cos…

A:

Q: Determine the general solution to (D² + 4)(f) = sin(2x) satisfying the initial condition: f (0) = 0,…

A:

Q: Consider the D.E. y(ª) + 4y" = 1 – cos(2x). Then a suitable form of the particular solution can be…

A: let the non homogeneous differential equation is of the form  y '' + p (t) y' + q (t) y = g (t)…

Q: fz = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O2…

A: Differentiate wrt t

Q: y(4) – 4y" + 4y" – 16y' = 4x? 3xe4 + 2 cos 4x -

A: The solution are next step

Q: What is the solution of the D.E y"-3y' e* sinx when solved using the %3D method of undetermined…

A: When a linear ordinary differential equation contains zero in the right-hand side of the equation,…

Q: 3. Describe whether the first order type: Linear or Exact and then solve to find the general…

A:

Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y dt O a. æ(t) = et…

A:

Q: Consider the following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t),…

A:

Q: Which of the following is the correct form of the solution to the non- dy homogeneous equation for…

A: Explanation of the solution is given below...

Q: The general solution to the second-order dif￾ferential equation d^2y/dt^2− 2dy/dt+ 7y = 0 is in the…

A: Given differential equation,  d^2y/dt^2− 2dy/dt+ 7y = 0 The general is of form,  y(x) = e^αx (c1…

Q: -Зп 3 cos? x sin x dx 3 cos?x sin x dx 4. a. b. 2т f(1 + t*)³ dt F(1 + t*)³ dt 5. a. b. •Vī t(1² +…

A: 4. We have to evaluate the values of   (a). (b)

Q: Obtain the required solution based on the given equation and condition (if there's any). 1) 4xdy –…

A: Using Variable Separable Method.

Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: Which of the following differential equations is exact? O (cos xy + xsiny) dx + (y – cos x + sin y)…

A:

Q: By using convolution find L{Sf e*cos(t – T)dr} Lütfen birini seçin: А. 3s (s+3)(s² +1) O B.…

A: We will find out the required value.

Q: 41. * + 4x + 5x = 8 sin t ; when t = 0, x = 0, x = 0. Note that i = is a common notation when the…

A:

Q: Q1-Find dy / dx for the following functions : e0 -2 2.8ln2 Y: Cosh9x * Inxy 4 6. cos0 log2 2 Q2-…

A: By bartleby rules, only Q1 has been answered.  Given function is…

Q: Which of the following is a differential operator that annihilates the function y= 5x* + Sx2 +6r +5…

A: The given function is, y=5x4+5x2+6x+5 cos4x+4ex2 Some properties. (1) If L1 annihilates a function…

Q: Which of the following is the form of a particular solution of y" +4y' = 3e2 + cos 2t + t? At e" +…

A: Given differential equation is

Q: 2. f(t)=t cos 8t +2 3. f(t)=1** +a cosh /2t +bsinh 2t 4. -cos' (21)+e f(1) = %3D e 5. f(t)=-3t'e St…

A: Laplace Transformation: Given a function ft defined for all real t≥0, the Laplace transform of ft is…

Q: Solve the following. Additionally, comment on the behavior of the solu- tion(s) as t → o. (a) 3 2 4…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Exercise: Solve the following differential equations: dy sin? y 1- dx cos2 x 2 - (1+x?)dy – 2xy dx =…

A:

Q: Which of the following differential equations is separable? dy cos(ty) dt O dy = dt t cos(ty) dy =t+…

A:

Q: Q1: Find 1) l (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 0. 0. 4) l (3t5) 5) l (e5t + cos 3t)

A: We can solve these problems by Laplace transforms.

Q: Q4: Solve the following differential equation using Laplace transform d²y + 25y 10 (cos(5t) – 2…

A:

Q: Which of the following is the form of a particular solution of y" + 4y' = 3e2? + cos 2t + t? Ae2 +…

A:

Q: Find a differential operator that annihilates the given function x²e ¬*sin (2x). A ((D+1)²+ 2) 2 B…

A: The given function is  x2 e-(x) sin(2x) (.) Annihilating differential operator of x(n)       is…

Q: Solve the Bernoulli's equation given below: dy 2 dx -y cot2x = y' csc2x O A. [(y )^(- 2)] sin 2x = -…

A: Use Bernoulli theorem to solve

Q: Which of the following functions is a solution of dx =D12x dt 12x - 8y dy 16х - 4у dt O a. x(t) = e…

A:

Q: Which of the following is the Euler (Cauchy) differential equation whose general solution is y =…

A: As you post multiple question according to guidelines I only solve the first one. Please repost your…

Q: The first solution of the D.E. x²y'+ xy + (x² - )y=0 is Vi =X Then a second linearly independent…

A:

Q: Which of the following functions is a solution of da 12x – 8y dt dy = 16x – 4y dt a. e (t) = e?*…

A:

Q: 9. Find the general solution of the following second order ODE: d?y dy = 1 + t sin(t) dt2 dt Observe…

A:

Q: Solve the following differential cquations 1. x + x*y -sec(xy) Ans. sin x = 2x2 +C x +y Ans. y- tan…

A:

Q: Which of the following functions is a solution of da 12a – 8y dt dy 16x – 4y dt O a. a (t) = e*…

A:

Q: Find the solution to the following PDES: ди ди y ду Ans. u = C;(xy): X dx k 2 dx- ди k > 0 at Ans. u…

A: The given problem is to find the solutions for the given partial differential equations.

Q: The function y = Cị cos(3x) + C2 sin(3x) is the general solution of a) Oy" – 9y = 0 b) Oy" + 9y = 0…

A:

Q: 10. Solve the following ODES by separating variables (a) dx Cos 5t where x(0) = 1 dt x2 (Ъ) dy e2y+t…

A: Given: (a) dxdt=cos5tx2 where x0=1  (b) dydt=e2y+t To determine: The solution of given ODEs by…

Q: Consider the following IVP: " + 4x = t+4; x(0) = 1, x'(0) = 0 Find the general solution. (A x(t)…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.