To find a particular solution of the form Yp = u1y1 + u2y2 of a nonhomogeneous DE using the variation of parameters method with W2 -2x = -e and W = 3e*, || we have Select one: — Зх ə = 7n C None of these 1 3x U2 - 9 1 -3x u2 O u2 = -e³x

Q: Consider the initial-value problem y = 6x + y, y(0) = 7. Calculate the first step only (i.e., y₁) of…

A: Given  y'=6x+y=f(x, y) y(0)=7 h=0.1 We have to find y1 =y(0.1)

Q: Find a general solution of each reducible second-order differ- ential equation y" + (y')² = yy'

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Q: 6 The non lin ear SYStem 2 2 5 x, - X2 =0 » Xx-Q.25(Sin X, + cCos X2)=0 has solution near

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Q: Show that the equation x2 + y2 = 2003 has no solutions in theintegers.

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y'= eV1--, y(0) = 0…

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Q: Let 47x + 20 y = 2 is a linear Diophantine equation 1) Show that 47x + 20 y = 2 has integnl…

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Q: Find a homogeneous LDE with constant coefficients that has y= - 3xsin2x as a particular solution.

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Q: Use the Gauss-Seidel iterative technique to find the 3rd approximate solutions to 2x1 + x2 – 2x3 = 1…

A: we take x1=w, x2=y, x3=z So we need to solve the system  2w+y-2z=12w-3y+z=0w-y+2z=2 Starting with…

Q: A 2nd order homogenous LDE has a solution xe-3x Find its general solution.

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Q: Use the Newton Raphson Method with XO=[-1 -2 1]' to approximate the solution to the given nonlinear…

A: Given a nonlinear system, Let  fx1,x2,x3=x13+x12x2-x2x3+6gx1,x2,x3=ex1+ex2-x3hx1,x2,x3=x22-2x1x3-4…

Q: 4+ Out X=U -3n,t Ox-2n3=6 + Yx2-2n3

A: x1+0x2+x3=4............i-3x1+0x2-2x3=6........iix1+4x2-2x3=-3............iii Now, converting given…

Q: Consider the initial-value problem y = 3x+y, y(0) = 5. Calculate the first step only (i.e., y₁) of…

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Q: #4. Starting with (1, 1, 1)', carry out four iterations of Quasi-Newton method to approximate a root…

A: Use the following formulae, to find the approximate solution of the non-linear system by the…

Q: 6. Use the Euler's method to obtain a MATLAB graph of an approximate solution of the initial dy…

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Q: Use Euler's method with step size 0.3 to compute the approximate y-values y(1.3) and y(1.6), of the…

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Q: Solve the nonhomogeneous IVP using the method of undetermined coefficients: y" +4y = x - 2cos 2.x,…

A: To solve the given Homogenous IVP using the method of undetermined coefficients.

Q: 5. Apply the Euler-Cauchy method with step length h to the problem y'=-y, y(0)=1 h = 0.1

A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = eV1--, y(0) = 0…

A: Existence of solution If f is continuous on an open rectangular interval R{a<x<b,c<y<d}…

Q: Find a general solution of each reducible second-order differ- ential equation y" = 2y(y')3

A: Given the differential equation:

Q: Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A?…

A: given a matrix A of order 2×2 ,  Av→=3v→ for v→=-1-1 (a) how is the pair 3,v→ called for a matrix A…

Q: Find a general solution of each reducible second-order differ- ential equation yy" + (y')² = 0

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Q: e) y-2y'+y

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Q: When does an nth order, homogeneous, Cauchy-Euler equation anty(n) + an-1tn-ly(n-1) + +aity' + aoy =…

A: Given: nth order To find: Cauchy-Euler equation

Q: Solution: y1 = 1.200000000; y2 =2.085625000; y3 = 3.079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: To find a particular solution of the form Yp = U1y1 +U2y2 of a nonhomogeneous DE using the variation…

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Q: 6. Use Cauchy-Euler equations solution method to solve x³y"' + xy' – y = 0 а.

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Q: If yp=e4x is a particular solution of nonhomogeneous DE y’’-4y=12e4x and yp=x is a particular…

A: Note that if y1 is a particular solution of a nonhomogeneous ode y'' +p(x) y' +q(x)y=r(x) and y2 is…

Q: 1. 2xy'+ xy'+ (x² 3) y=O a) Show thet a regulor singulerity Xa>0 is point. 6) Use froteniaw method…

A: (a) Given equation, We know that,

Q: 3t yy"2y

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Q: 3- Find non-zedo solution ofs dy

A: we need to solve the given first order nonlinear differential equation. The given equation is…

Q: Find the particular solution that satisfies the initial condition.

A: Afghan

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

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Q: Use jacobi method to find approximate solutions to 20x+2y+3z=25 3x+10y-4z=9 2x-y+5z+6 starting the…

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Q: 7. Use Newtons method with the given X(0) to compute X(2) for each of the following nonlinear…

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' eV1 guaranteed by…

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Q: Consider the following initial value problem 0 if x <-1 Ut + 3uu, = 0, u(x,0) = 1 otherwise. 1 if x…

A: Consider the following Initial value Problem : i. ut+3uux=0, u(x,0)=0if x≤-11otherwise. The…

Q: Use Euler's method to approximate the solution of the following initial-valu

A: Given,         y'=y2t+1, 0≤t≤1, y(0)=1, with h=14 and  t=12

Q: 1)Show that the forward Euler method applied to the following IVP is stable: y' = 2y – t, y(0) = 1.…

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Q: yp=u1x+u2x^-2 is the particular solution proposed for the nonhomogeneous Cauchy-Euler equation…

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: The van der WVaals equation of state is given by 3. (P +) (v- b) = RT In this equation, v (V/n)…

A: This is a multipart question having 3 or more interrelated subparts. So, as per the company policy,…

Q: Use the Newton Raphson Method with X0=[-1 -2 1]" to approximate the solution to the given nonlinear…

A: Solution: The system is x13+x12x2-x1x3=-6 ex1+ex2-x3=0 x22-2x1x3=4 Suppose that…

Q: 3. Find the general solution to the second order nonhomogeneous linear equa- tion y" +y/ - 2y = 6et.

A: To find the particular solution use the method of undetermined coefficients. Since e^t appears in…

Q: > Reduce the fellouing partial diffrential equation ith constant cobficients into canmonical form…

A: A=4, B=5, C=1, then B2-4AC=25-16=9&gt;0 So, the given pde is the hyperbolic pde. Step 1: We will…

Q: Find the general solution of I' = -1 Discuss the type and stability of the critical point (0,0) as…

A: Given xι= a1-1ax  Let the given matrix be A=a1-1a Now we have to find eigen values first,…

Q: (2) Find the solution with initial condition (6,6).

A: This is a problem of system of differential equation.

Q: Consider the initial value problem (IVP) given by y" – 4y = e-", y(1) = 1, y/(1) = 0. (*) (a) Give…

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Q: 1. Use the method of reduction of order to find a second solution y2(x) and a particular solution…

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Q: to find a Use the method of frobenius solution of the fallowing DDE: near

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