Given f(2) = . t2 – 1 dt 1+ cos?(t) At what value of x does the local max of f(x) occur? x =

Q: Given a function : E = 1/2 mv^2 + 1/2 kx^2 Where, x = A cos(wt) v = dx/dt k= mw^2 A, w are constants…

A: Given information: The function is E=12mv2+12kx2, and the value of x=A cos(wt), v=dxdt and k=mw2. To…

Q: Find general solution for y"+y=0.5cos(t) and state whether it is undamped, underdamped, critically…

A: The second order non-homogeneous  differential equation is y''+y=0.5cos(t) Solution for second order…

Q: Find the particular solution for f(x) with the given initial conditions. f''(x) = 4x3 and f'(1) = 5…

A: Given,           f''x=4x3  and f'1=5  and f0=50

Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: Q1-Find dy / dx for the following functions : * -2 2.8ln2 Cosh9x, * Inxy 2 Y= 4 3 6. sino 5 log22…

A: We have to solve given problem:

Q: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

A:

Q: Solve the initial value problem for an arbitrary f(t) function. y"+4y'+4y=f(t),  y(0)=2 ,  y'(0) =…

A:

Q: 14. Solve the equation d?x 3 +2x sin dt2 dt dx given that at t = 0, x = 0 and 1. dt nent

A: See the details solution in below

Q: Find the differential co-efficient for the following equations i. f(x) = x20 ii. f(x) = (2x³ – 3x² –…

A: Given: i.  f(x)=x15x32x20ii.  f(x)=(2x3−3x2−10)−45(5x2+4)+e9xiii.  f(x)=x7+e−7x−xlogx+3e−10x

Q: If the function f (x) solves the initial value problem dy E (х + 1)-И dx -1/2 IT • cos(TX)

A: Givendydx=x+1-1/2-πcos(πx)

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

A:

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1)- = 3, x(2) = 0 dt

A:

Q: Find the function f(x) described by the given initial value problem. f"(x) = 7 sin x, f'(T) = -5,…

A:

Q: If the function f (x) solves the initial value problem dy = (x +1)-1/2 – T · cos(T2) y(3) = 2 , %3D…

A: Given: dydx=x+1-12-π·cosπx Now separate the variables; dy=x+1-12-π·cosπxdx Now taking integral on…

Q: Solve the following initial value problem: Cos(t)² dy 1 dt

A: "Since you have posted multiple questions, we will answer the first question.  If you want the…

Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt  ,   P(t) = 5Re-tRC2×R

Q: Find the function f (x) described by the given initial value problem. f"(x) = 5 sin x, f'(T) = -5,…

A:

Q: Solve the initial value problems for x as a functionof t. (t + 1) dx/dt = x2 + 1 (t > -1), x(0) =…

A:

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

A:

Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: Which of the following is the c value obtained for the special solution of the equation y'=ex+y…

A:

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: Find an explicit solution of the given initial-value problem, and define the exact interval I of the…

A:

Q: 1-cos (t) B: Solve the D.E ý + 2ý + y = with zero initial conditions

A: Given y''+2y'+y=1-costt2with zero initial condition, i.e. y0=y'0=0

Q: Solve the initial-value problem for a as a function of t. dr 9, x(2) = 0 (2t* – 212 +t – 1) dt

A: We have to solve the initial value problem

Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: t2+2tdxdt=2x+2 ; x(1)=1. Find the solution of this initial value problem.

Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

A:

Q: (c) Use the substitution x = e', (x > 0) to transform the following Cauchy-Euler equation to a…

A: Given equation is x2y"-xy'+4y=sin logx+xcoslogx Here, we need to use the substitution x=et to…

Q: QUESTION 4 Given f(x) = 8x3 + 2x. Estimate the value of f(2.01) using differential.

A: Given that: f(x)=8x3+2x

Q: 1) Determine f(x) given its rate of change, and that satisfies the given initial conditions: f' (t)…

A:

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin a, f(0) = 2 f(x) =

A:

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin x, f(0) = -6 f(x) =

A: This question is based on application of integration.

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1) - 3, г (2) — 0 dt

A:

Q: 4. Show that :| f(t) sin a(x – t)dt Y : solves the initial value problem dy +a²y = f(x), dx? dy 0…

A: Below is the answer

Q: Solve the initial value problem. ds = Cos t - sin t, s dt = 4 %3D

A: According to the company policy, I'll solve the first question. Please resubmit the second question.…

Q: B- Solve one of the following initial value problems for y as a function of x: 2. =- 1, y(0) = 1 dy…

A:

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin r, f(0) = 3 = sin…

A: NOTE: Refresh your page if you can't see any equations. . take integration  .................(1)

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: 1. Verify the initial value theorem for the voltage functions: a. 4+2 cos(t) b. t - cos (3t) and…

A: Given functions are a 4+2costb t-cos3t

Q: Find the function f(1) described by the given initial value problem. f"(z) = 6 sin z, f'(m) = 4,…

A:

Q: Find the general solution using the method of variation of parameters of the following: (2) y" – 3y'…

A:

Q: (c) Use the substitution x = e', (x > 0) to transform the following Cauchy-Euler equation to a…

A:

Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

A:

Q: Solve the initial-value problem for y as a function of z. (64 – ) = 1, y(0) = 2 dy da

A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS * for partial derivative symbol, use the letter d 05…

A:

Q: Solve the initial-value problem for a as a function of t. da 9, x(2) = 0 (2t – 212 +t – 1) – dt

A: We have to solve the initial value problem for x as a function of t.…

Q: Verify if the given function is a solution of the indicated differential equati 1. y = In sin( x +…

A: Since you have asked multiple questions in a single request. so we will answer only the first…

Q: Find general solution for y"+2y'=t², y(1)=0, y'(0)=-1 and state whether it is undamped, underdamped,…

A: