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Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .. an are fixed constants. Consider the nth...
Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .....
Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .. an are fixed constants. Consider the nth order linear differential equation L(y)=4e9x cos x + 5x20 (*) Suppose that it is known that Llyi(x)]=6xe9x Lb'2(x)] = 6e9x sinx し[y3(x)]-6e9x cos x yi(x)-1 2xe9x y2(x) = 42e9x cosx y3(x) 60e9x cos x + 180e9x sinx when when when Find a particular solution to (*)
Empty Part only Let L[y]: y"" y'+4xy, yi (x): = sinx, y2(x): =x. Verify that L[y11(x)...
Empty Part only
Let L[y]: y"" y'+4xy, yi (x): = sinx, y2(x): =x. Verify that L[y11(x) 4xsinx and to the following differential equations. Ly2 (X)= 4x1. Then use the superposition principle (linearity) to find a solution (a) Lly] 8x sin x - 4x2-1 (b) Lly] 16x+4 -24x sin x y1(x)- cos x tlV]¢»= 4x° Substituting yi (x), y, '(x), and y"(x) into L[y] y""+y' +4xy yields Lfy1(x) 4xsinx. Now verify that +1. Calculate y2'(x) y2'(x) 1 Calculate y2"(x). У2"(х)%3D 0...
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1...
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...
we assume that X solves the differential equation X'=AX. In this problem, we will investigate the strategy to deal...
we assume that X solves the differential equation X'=AX.
In this problem, we will investigate the strategy to deal with repeated eigenvalues. Conside:r A=17-2-6 1. This matrix has only one eigenvalue Ao of multiplicity 3. Find the characteristic equation, the eigenvalue λ0 and an eigenvector P for λ0 2. Find vectors K. L such that (A-X0IK-P and (A-X01)L-K. Compute the matrix M-1AM where M-(PIKL) 3. Let Y -M'X. Solve the equation for Y in the following manner : first, solve...
9. Superposition Principle: Let L[yl=y" + y + xy, yı(x)=sinx ^yz(x)=x.If L[y] x = xsinx and...
9. Superposition Principle: Let L[yl=y" + y + xy, yı(x)=sinx ^yz(x)=x.If L[y] x = xsinx and L(y2 x)=x²+1 then use the superposition principle to find a solution to the differential equation: L[y]=4x²+4-6 xsinx
NOTE: h=(b - a) / N Consider the differential equation y" y' +2y + cos(), for...
NOTE: h=(b - a) / N
Consider the differential equation y" y' +2y + cos(), for 0 x , with boundary conditions (0) 0.3, Show that the exact solution is (x)(sin3 cos())/10. (a). Consider a uniform grid with h (b? a)/N. Set up the finite difference method for the problem. Write out this tri-diagonal system of linear equations for yi, (b). Write a Matlab program that computes the approximate solution yi. You may either use the Matlab solver to solve...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be a...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0)...
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0) = x3 + 1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
I need help solving these problems 1. Suppose that y= a (x-1)" is the power series...
I need help solving these problems
1. Suppose that y= a (x-1)" is the power series solution of the following initial value problem. x-y+2y=0; y(t) = -2, y(1)=1 Find the value of az. 2. Suppose that y=0(x) is the solution of the following initial value problem. y" + xy - (sinx)y=0; y(0)=1, 7(0) = 3 Find the value of (0) 3. Let p be the radius of convergence for the Taylor series of the following rational function centered at the...
Let βˆ = (X′X)−1X′y where y ∼ N(Xβ,σ2I), X is an n×(k+1) matrix, and β is a (k+1)×1 vector. Are βˆ′A′[A(X′X)−1A′]−1Aβˆ a...
Let βˆ = (X′X)−1X′y where y ∼
N(Xβ,σ2I), X is an n×(k+1) matrix, and β is a (k+1)×1 vector. Are
βˆ′A′[A(X′X)−1A′]−1Aβˆ and y′[I − X(X′X)−1X′]y independent?
Let B (X'X)-X'y where y ~ N(XB,02I), X is an n x (k+ 1) matrix, and B is a (k+1) x1 vector Are BA A (X'X)-A]-AB and yI - X(X'X)-xy independent?
Let B (X'X)-X'y where y ~ N(XB,02I), X is an n x (k+ 1) matrix, and B is a (k+1) x1 vector Are...
Let Uy) = any(n)(x) + an-1 y(n-1)(x) + + ai y'(x) + aoy(x) where ao.a1, .. an are fixed constants. Consider the nth order linear differential equation L(y)=4e9x cos x + 5x20 (*) Suppose that it is known that Llyi(x)]=6xe9x Lb'2(x)] = 6e9x sinx し[y3(x)]-6e9x cos x yi(x)-1 2xe9x y2(x) = 42e9x cosx y3(x) 60e9x cos x + 180e9x sinx when when when Find a particular solution to (*)
Empty Part only
Let L[y]: y"" y'+4xy, yi (x): = sinx, y2(x): =x. Verify that L[y11(x) 4xsinx and to the following differential equations. Ly2 (X)= 4x1. Then use the superposition principle (linearity) to find a solution (a) Lly] 8x sin x - 4x2-1 (b) Lly] 16x+4 -24x sin x y1(x)- cos x tlV]¢»= 4x° Substituting yi (x), y, '(x), and y"(x) into L[y] y""+y' +4xy yields Lfy1(x) 4xsinx. Now verify that +1. Calculate y2'(x) y2'(x) 1 Calculate y2"(x). У2"(х)%3D 0...
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...
we assume that X solves the differential equation X'=AX.
In this problem, we will investigate the strategy to deal with repeated eigenvalues. Conside:r A=17-2-6 1. This matrix has only one eigenvalue Ao of multiplicity 3. Find the characteristic equation, the eigenvalue λ0 and an eigenvector P for λ0 2. Find vectors K. L such that (A-X0IK-P and (A-X01)L-K. Compute the matrix M-1AM where M-(PIKL) 3. Let Y -M'X. Solve the equation for Y in the following manner : first, solve...
9. Superposition Principle: Let L[yl=y" + y + xy, yı(x)=sinx ^yz(x)=x.If L[y] x = xsinx and L(y2 x)=x²+1 then use the superposition principle to find a solution to the differential equation: L[y]=4x²+4-6 xsinx
NOTE: h=(b - a) / N
Consider the differential equation y" y' +2y + cos(), for 0 x , with boundary conditions (0) 0.3, Show that the exact solution is (x)(sin3 cos())/10. (a). Consider a uniform grid with h (b? a)/N. Set up the finite difference method for the problem. Write out this tri-diagonal system of linear equations for yi, (b). Write a Matlab program that computes the approximate solution yi. You may either use the Matlab solver to solve...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0) = x3 + 1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
I need help solving these problems
1. Suppose that y= a (x-1)" is the power series solution of the following initial value problem. x-y+2y=0; y(t) = -2, y(1)=1 Find the value of az. 2. Suppose that y=0(x) is the solution of the following initial value problem. y" + xy - (sinx)y=0; y(0)=1, 7(0) = 3 Find the value of (0) 3. Let p be the radius of convergence for the Taylor series of the following rational function centered at the...
Let βˆ = (X′X)−1X′y where y ∼
N(Xβ,σ2I), X is an n×(k+1) matrix, and β is a (k+1)×1 vector. Are
βˆ′A′[A(X′X)−1A′]−1Aβˆ and y′[I − X(X′X)−1X′]y independent?
Let B (X'X)-X'y where y ~ N(XB,02I), X is an n x (k+ 1) matrix, and B is a (k+1) x1 vector Are BA A (X'X)-A]-AB and yI - X(X'X)-xy independent?
Let B (X'X)-X'y where y ~ N(XB,02I), X is an n x (k+ 1) matrix, and B is a (k+1) x1 vector Are...
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