Question 1 : Use Runge – Kutta's method of order four to find an approximate value of y for x = 0.2 in step of 0.1 if 2 = x² + y², y(0) = 1. dx

Q: Question 5 Evaluate the multiple integral | cos(x - y) dx dy

A:

Q: Question 19 Find the solution. y3 y (0) = 1 dy dx 1-2xy2 A yx²– In lxl=0 B -xy²+ In Ixl=0 © 2ry2+ In…

A: Given differential equation is dydx=y31−2xy2......1 and y0=1. We have to find the solution of the…

Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

A:

Q: QUESTION 3 x"+x'+3tx³ = 2et x(0) = 3 x'(0) = 4 %3D %3D At = 0.2 %3D Use the Euler method with a time…

A: Euler's Method: Euler's method is used to approximate the solution of differential equation of the…

Q: Question 6. Using a suitable linearization to approxi- 1 show that mate 1.02 (i) The approximate…

A: (i) To approximate 11.02 using suitable linearization, consider a function: fx=1xf1=11 Therefore:…

Q: Question 12 Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a…

A:

Q: Question 11 Consider the equation 6xy dx + 5(x² + y) dy=0. Following the technique of finding an…

A:

Q: QUESTION 5. Use the fourth order Runge-Kutta method with h = 0.25 to approximate (to 6 decimal…

A:

Q: a n п i = 6 dz EVALUATE IN TERMS OF GAMMA FUNCTION.

A:

Q: Question 3: a) Find Y(s)/ X(s) for the following differential equation d'ydy dy d?x dx +2+9x, where…

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: QUESTION 1 Consider the IVP: x" + (x')? + 4tx=0, x(0) = 1, x'(0) = 2 Using the Euler method with a…

A:

Q: Question 5 Determine whether the equation exact. Otherwise, find an integrating factor that will…

A: Topic - differential Equation

Q: Question 12 If L{f (t) }= | e-(s+1)! ¡2sin²4 dt_then what is f (t)? ,- (s+1)! ¿2sin²t dt, then what…

A:

Q: QUESTION 1 (a) Given y=cosh (x-3). Based on the given function show that d'y d'y 4 sinh (2x) ) dx''…

A: Given that, y=cosh2x-3 To prove, 14sinh2xd3ydx3+d2ydx2-tanhx-3dydx=2y+1  But i think it should be,…

Q: Question 12 Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(O) = 0 Find the general solution.…

A:

Q: Let H(t) denote the Heaviside step function. Find (a) L[H(t – 1/2) cos t]

A: As per the guidelines I am supposed to do the first question only. Kindly repost the other questions…

Q: QUESTION 4 x' = -2x + 4y y' = 4x - 5y x(0) = 1 y(0) = 3 At = 0.1 %3D Use the Euler method with a…

A: Given  system of differential equation is, x'=-2x+4y and y'=4x-5y. With initial conditions, x0=1 ,…

Q: Question 6 of 7 View Polices Current Attempt in Progress 1. Find the local linear approximation of…

A:

Q: Question 3. Use Newton's divided difference method to compute the voltage att=0.045 from the…

A: To use Newton's divided difference method, first we will find out the divided difference table : For…

Q: Question 5 The Integrating Factor for the DE y dx = (ye-2x)dy is 2y -2y None of These

A:

Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

Q: Question 8 Evaluate. The differential is exact. (6, 9, 8) (5x + 1)ex dx + z dy + y dz (0, 0, 0) 6e…

A: A parametric equation defines a group of quantities as functions of one or more independent…

Q: dy .2 +3x² = dx 6x, y(0)=3 with step size a) Ar=1 b) Ar = 0.1 %3D c) Ar = 0.01

A: We can solve this problem by Euler's approximation.

Q: Question 4 a. Solve the following definite integrals. xp (* + x^€) ,'J (V&+1)* dx

A:

Q: Question 7 The equation characterizing the plane tangent to the graph of the function f(x, y) = log…

A:

Q: Question 16 Use the table below and the trapeziod method with n = 5 to approximate (x) dx. f (x) 4.2…

A: Given that  From the table  Use trapezoidal rule to determine the integral

Q: Question 12 The Integrating Factor for the DE y dx = (ye-2x)dy is None of These 2y -2y

A:

Q: Question 1. Find the linearization of the function y = f(x) = x² sin(x) at a = T/4 and use it to…

A: Linearisation of f(X) at a is given by-  L(X) = f(a) + f'(a)(x-a)

Q: the initial value 2. Find the solution to problem. y' + () y = Cos t y(T)=0, t>o %3D

A:

Q: Question 3 6x³e**3 dx. using integration by parts Svdu) and letting = UV u= f(x), dv= 3 g(x) dx,…

A:

Q: QUESTION 4 The minimum value of n required to approximate dx by composite Trapezoidal rule xe with…

A:

Q: Solve the initial value problem + x = Heaviside (t – 5), x (0) = 14, dt? dx (0) = 2 Important: Use H…

A:

Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

A:

Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

A:

Q: QUESTION 3 x" +5x' + 4x = 12t + 30 e, x(0) = 1, x'(0) =3 Solve the above IVP and then find x(0.25).…

A: The given differential equation has been solved in step 2 and step 3.

Q: Question 2. By employing Euler's method with step size h=0.25, find the numerical solution of the…

A: Question 2.  Given, y'=1+yx, y1=2, h=0.25, y2.5=? Euler method,…

Q: QUESTION 11 dz = = zP z1- -i (-e2 – 1)i e (e? + 1)i e (e? – 1) ei (e2 – 1)i e

A:

Q: QUESTION 3 Suppose that z= xy, where x=2t+4 and y=s+3t. Find Oz at the point (s.t) = (5, - 1) at Oa…

A:

Q: Question 6 of 13, Step 1 of 1 Co Consider the function u = (-3t + 6)2. Find the differential for…

A: We can find the differential as below.

Q: QUESTION 1 Solve the following first order pde by the method of characteristics: du at du + X = 2xt…

A:

Q: QUESTION 5. Use the fourth order Runge-Kutta method with h = 0.25 to approximate (to 6 decimal…

A: Given : y'=-2xy      y0=1              0≤x≤1            y0=1    x0=1    h=0.25 TO Find : Approximate…

Q: Question#1(a): Calculate | F.dr for the following F = 2z,x,- y , C :r = cost,sin t, 2t from 0,0,0 to…

A:

Q: Question 7 OT 15, Step Correct Consider the function y 3x + 5x2 + 4x - 2. Find the differential for…

A:

Q: Question 6 Differentiate: y = arccot (x) + arctan 2 + x 1 - 2x 0 1 (E) None of these O:2x O 1-2x

A:

Q: Question 27 Which of the following methods can be applied to find a particular solution y, of y"…

A:

Q: 3. A particle moving in a straight line has acceleration, a(t) = 10 sin t + 3 cos t, with initial…

A:

Q: QUESTION 3 For the IVP dy =x(x+y), y(2) = 2, by Euler's method y(2.5) = dx %3D 04 0 8 o None of…

A:

Q: Question 6 Consider the equation и, — kuxx — и%3D 0. - v(x,t)eat for s suitable a e R, reduce the…

A: Consider the given equation ut-kuxx-u=0. Let ux,t=vx,teat. Differentiate with respect to t as…

Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).