Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A) y(t) = 2cos t + sinh t– 2cosh t B y (t) = 2sinh t + cosh t- 2cos t y (t) = 2cosh t + sinh t– 2cos t y(t) = 2cosh t + sinh t- 2sin t

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

A:

Q: y -cx'y' +e +sin(xy) – (ny + y) =0 y' =?

A:

Q: y"+ 10y'+25y=2e¯ 1. where y (0) =0 and y'(0) =1

A:

Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

Q: 3. y" +2y' + y = 2 sin t H(t – n), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost+ (t+1-)e™-']H(t–n) %3D

A: The given differential equation is: y''+2y'+y=2 sin(t) H(t-π) ;              y(0)=1,   y'(0)=0

Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

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: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

A:

Q: y +y=y² 1 ソ= ce* +1 4.

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Use RK2 (Heun's method) with h = 1/4 to estimate y(4/4) given Yo 30: Y1- Y2: Y3- Y4: 3/13 3/2: Y'3:…

A:

Q: Particular Solution   cot x (y' + 1 ) 2y = 0, y (π/4) = 9

A:

Q: Define diffeomorphish between two manifolds and Completly explain why any linear map fiM_N. between…

A:

Q: x" - 3x' + 2x = - 8t, x(0) = 2, x'(0) = 6 Solve the above IVP and then find x(0.25). Put x(0.25)…

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: 7. Given: y = 3 ; Find: dy/dt V16+tª -613 (16+t*) -2t3 (16+t*) (16+41) 글 (16+t*) ? (E) None of the…

A:

Q: y" + 3y' + 2y = cos(e).

A:

Q: 4. Find the solution for the following b. y' + 2y't y = cost y) = 1, y ²) = 2

A:

Q: Solve y(t) – [ (1+u)y(t – u)du = 1~ sinh t

A: Consider the given:…

Q: find the solution yll +2y' +2y=e-t, y(0)=0, y' (0) =0 -2t e-t +cost a e-t-e-t cost b0 e-t-e-2t +cost…

A:

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

A:

Q: Solve the initial value problem y" + 12y' + 37y = 0, y(0) = 1, y'(0) = 0 O y = 6e-6'cost + e-6f sint…

A:

Q: Find a particular solution for: y" - 3y' + 2y = te*

A:

Q: The following are three different methods for solving y (t) = f(t, y(t)): (A) Yn+1 = Yn + ¥ [S(tn,…

A: Given : three different methods for solving y't=ft,yt : A yn+1=yn+∆t2ftn,yn+ftn+∆t, yn+∆t ftn,ynB…

Q: y" + 6 y' + 9y = 0 ; y(0) = 1 and y'(0) = 2 %3D %3D Ans: у %3 (1 + 5х) е

A: To find: The particular solution of the given differential equation. Given information: The…

Q: y? when y dy and x = 1. Find the particular solution to dz

A:

Q: ) Using Huen's method to estimate the solution of the ODE y' = cos (xy?) ,y(1) = 2, h = 0.1 If y1=…

A:

Q: 3. y"+2y' +y = 2 sin t H(t – x1), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost + (t+1-1)e"-']H(t-x)

A:

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: 1. y"+y'-6y= -10-

A: As per our guideline we can solve only first question for you. Since all are separated questions.…

Q: y" – y' = sin(t) y(0) = 1 y' (0) = -1

A: We have to solve the IVP           y''-y'=sinty0=1y'0=-1

Q: Find the solution for the following IVP: y+3y=2x-1, y(0) = 3

A: