The following initial-boundary value problem for the heat equation. du =-2 cos p- 5, 0 0 u(0,t) = u(2,1) = 1, t20 u(x,0) = sin 2ax+ cos Tx i. By using finite difference method with step size At = 0.01 and Ar = 0.4 , show that U;r41 =(-0.125 cos p)u,1, +(1+0.25cos p)u;, - (0.125 cos p)u1, 11. Hence, by taking p= n, solve the heat equation above up to t= 0.01.

Q: (f) dx /3 — 2х — г?

A: Question f,Given,           ∫x3-2x-x2dx

Q: = 1- Solve y"+6y' +9y=2xe * + 3 + 2x²

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

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: 11. Let {(x, y) : x² + y² < 1} D = be the unit disc and f(x, y) = x² – 2x + y² + 2y + 1. Find the…

A:

Q: H. JJ HY BY 4.6 where y(0)=0 y'co)=2

A: Given differential equation is y''+4y'+3y=4e-x with y(0)=0 and y'(0)=2We know the formula that PI of…

Q: If y satisfies the IVP dy dx then y(n-1) = O A.-0.46 = cos x, y(0) = -1, OB.-0.26 OC -0.36 O D. none…

A:

Q: - 5x² + 2y? = 4 5y² + 3 = x² sin(x + y) = 2x

A: According to guidelines we can answer only three subparts, or first question and rest can be…

Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

A:

Q: Find f. f"(0) = sin(0) + cos(0), f(0) = 1, f'(0) = 4 %3D %D

A:

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Use Euler method to approximate the value of y(0.1), given               y' - x2 - y = 5 ,  y(0) =…

A: Euler Method:-  For a function fx, y the method is xi+1=xi+∆xyi+1=yi +h fxi, yi; i=0, 1, 2,... Here,…

Q: 5. A tank contains 100 gal of water and 50 lbs of salt. Water containing a salt concentration of (1…

A: (a)Given that a tank contains 100 gal of water, and 50 lbs of salt.The water with the salt flows in…

Q: (D² + D)y = 81r² +14 cos(4x) where y(0) = 0 and y'(0) = 3 %3D

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: y = C¡e e-2= + Cze³* + C2e%

A:

Q: dy Q1/ Find dx 1. if y = u and u 4x2-2x +5. %3D 2. y = (x2 + 4)2(2x3- 1)3 %3D 3. xy + x- 2y- 1 = 0…

A:

Q: H.W: Find y' 1.y sin V2t 2. y=cos (1/x) 3. y sec (2s +1) !! 4. y= cos 1 x 5.y tan V3x 8. y=csc (x²…

A:

Q: Which of the following nonhomogeneous equation cannot be solved the method of undetermined…

A: If the term in the non homogeneous part is of the form eax, sinax, cosax, x,x2,..., xn, then the…

Q: 2. Solve for y in the equation y = e* sin x + e* cos x – y +c 3. Solve for f e* sin x dx in the…

A: Given, (2) y = exsinx +excosx -y +c  We have to solve for y (3) ∫ex sinx dx = ex sinx + ex cosx -…

Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

A:

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: 8. Consider the following model for the populations of two species in competition in a given…

A:

Q: Use any one method to find the PS of y" (x) + y"(x) = cos x " '(0) = y"(0) = y'(0) = y(0) = 0 %3D…

A: