(a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5 ras %3D 15 500 Note: By convention, we define In 0 = -o. %3D

Q: A 25–2 design was used to investigate the effect of A = condensation temperature, B = amount of…

A: Given: 25-2 design is given.The results…

Q: In each of the following find the pdf of Y. (a) Y = X? and fx(x)= 1, 0 < I< 1 (b) Y = - log X and X…

A:

Q: In VVi+1-2 dt, if we let V Vt+1 – 2, then dt is equal to A 2(x²+2)dx ® 4x(x²+2)dx c) None D…

A:

Q: The general solution of the DE y" -y" + y'-y 0 is Ye = C1 e* + C2 Ssin(x) + C3cos(x) None of These.…

A:

Q: 1.4 Using the graph in Figure 1.7 below, find Saf (t)dt and if the area of the shaded region is A,…

A: Given the graph representing the area

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to A (4x³ + 2) dx B) None 2(x²+2)dx D 4x³dx 4x…

A:

Q: 3. Solve the particular solution of the given D.E using the provided initial value condition: da * =…

A: According to question,Given differential equation,dxdt = 4x2 + 1 ;xπ4= 1

Q: Which of the following is the general solution of: y(x+1) 2 dy dx x Select one: O a. 2lny = x - ln x…

A: Given problem :- 2dydx=yx+1x

Q: Marked out of 2.00 lag question Find the integrating factor for (x-1) y' y +2 (x-1)3. OA. (x- 1) - 1…

A: Rewriting the given differential equation into standard linear differential equation

Q: e-x-y x> 0, f(x,y) = { e y >0 otherwise Then: O None of these ) X and Y are statistically…

A: Solution

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

A:

Q: In one model of the changing population P(t) of a community, it is assumed that = - , where and are…

A: According to question, dPdt = dBdt-dDdt

Q: In t+1-2 dt, if we let t+1-2, then dt is equal to A 2(x2+2)dx (в 4x³dx O 4x(x2+2)dx D None E…

A: Option C is correct.

Q: 1. Consider the simple pandemics model X+1 distributed over [e=1, e]. WkXk where {W1} is an i.i.d.…

A:

Q: v Assessment D ust.blackboard.com/ultra/stream/assessment/_5288785 1/overview/attempt/_236 OSettings…

A: The given differential equation,x4y2sinx-2ydx=xdy

Q: Find an implicit and an explicit solution of the given initial-value problem. (Use x for x(t).) dx =…

A: The given initial-value problem,dxdt=4x2+1, xπ4=1

Q: ate the order of the given (1-x)y" - 3xy' + 6y = cos x etermine whether the equation is linear or…

A:

Q: In each of the following, find pdf of Y a) Y= X2 and  fX(x) = 1, 0 0 c) Y = eX  and fX(x) = 1/σ2 *…

A: Given: Then:

Q: 7:31 MAC2311C-FINAL-A PDF - 234 KB 10 Problem 10. The value of the integral nz dx equals: (A) In 2…

A:

Q: Let y = y(x) be the solution to the initial value problem %3D dy ezty: dx y(0) = –1. %3D Find the…

A:

Q: The general solution for D. E. e'y'- + e = 0 is x++xy x- Inx|+c y = e + In x+y-1 Inx+c x+y-1 ソ= -x +…

A:

Q: f substance B, in milligrams, left after t years, given that the initial quar

A: Option of part c is A.

Q: 12 (a) Approximate dtwith a left hand sum and At = 2. t+2 12 (b) Approximate A t dt with a right…

A:

Q: 3. Solve the particular solution of the given D.E using the provided initial value condition: da =…

A:

Q: Solve the given initial-value problem. L (di/dt) + Ri = E,    i(0) = i0,    L, R, E, i0 constants

A: GivenL.didt+ R i =E  ,   i(0) =i0didt+RLi =EL---1It is linear differential equation of the form…

Q: Find an explicit solution of the given initial-value problem. dx = dt = 2(x² +1), x(77) = 1 11 X

A: Given :dxdt=2x2+1xπ4=1

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: If dx with initial condition y(2) = 1, then the value of C is equal: O 3 5/2

A:

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

A:

Q: 1 D = | (1+e*)³e' dt -1 E t In (t) dt 2 1 F In ( 1+ dt 1 G = t² In3 (t) dt 1

A:

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: Find solutions to the equation dt dX = k (a – X) (ß – X) governing second- order reactions in the…

A: We will use partial fraction method to solve the differential equation.

Q: Suppose that the specific growth rate of a plant is 1%; that is, if B(t) denotes the biomass at time…

A:

Q: This question is designed to be answered without a What is the particular solution of d = 2xy-y…

A: Solving the differential equation by seperation of variables.

Q: Example 10.17. Apply Runge-Kutta method to find approximate value of y for x = 0.2 in steps of 0.1,.…

A: Probem is solved using runge kutta method.

Q: 1. Given the PMF of dielectric constant k of a capacitor: a = 1,2 Px (k) = a = 3, 4, 5 O other wise…

A:

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Consider the following initial value problem d 4 y (z) + e" y (x) = cosh (x), y (0) = Without…

A: We have to find the value of first derivative and second derivative when x=0 without solving the…

Q: Solve the given initial-value problem. dx1 X1 (t) with x, (0) = - 3 and x2(0) = - 1. X2 (t) dt 3 12…

A:

Q: Find an explicit solution of the given initial-value problem. dx = · 3(x² +1), x(7) = 1 dt X =

A:

Q: Solve the initial value problem y" + 2y' +y = et+ 8(t – 3); y(0) = 0, y' (0) = 3. %3D - Justify your…

A:

Q: d If g(x): ªſ^*[e'− In(2t+1)]dt, find g''(x) . dx -2 A B == 4 (2x + 1)² 4 (2x + 1)² None of the…

A:

Q: A fish population in a lake satisfies dB/dt=cB(K-B) Fish are then added at A fish per hour.  Find…

A: Please check step 2 for solution

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Find the solution of the given DE [ d^(3) x / dt^(3) ] – [ 19 dx/dt ] + 30 = 0

A:

Q: X (1) is a WSS process with E [X (t)]=2 and Rxx (7) = 4 + e-0.1 14, Find the mear 1 and variance of…

A:

Q: 3. [MO51] Classify the following PDE as (i) Linear or Nonlinear, (ii) Homogeneous or nonhomogeneous…

A:

Q: Find an explicit solution of the given initial-value problem. dx/dt = 7(x2 + 1),    x x(?/4) = 1

A: Given an initial value problem : dxdt=7x2+1 Also x(4)=1 We need to find an explicit solution. Let's…

Q: 2. Does Picard's Theorem imply the following initial value problem has a unique solution? Explain y'…

A:

Q: Use the second-order predictor-corrector method (that is, the first-order Adams-Bashforth formula as…

A: Answer is given using second-order predictor-corrector method.