Find the solution of the initial-value problem X′(t) = ( −8 −5 5 2 )X X0...

Find the solution of the initial-value problem X′(t) = ( −8 −5 5 2 )X X0 = ( 0 1)

Expert Solution

milcah answered 2 years ago

Homework 1.1. (a) Find the solution of the initial value problem x' = x^(3/8) , x(0)=1...

Homework 1.1. (a) Find the solution of the initial value problem x' = x^(3/8) , x(0)=1 , for all t, where x = x(t). (b) Find the numerical solution on the interval 0 ≤ t ≤ 1 in steps of h = 0.05 and compare its graph with that of the exact solution. You can do this in Excel and turn in a printout of the spreadsheet and graphs.

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value...

1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value problem. yy'=e^x+x , y(0)=y_0 y_0 is a nonzero constant.

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Find the solution of the initial-value problem. y'' + y = 3 + 5 sin(x), y(0) = 5, y'(0) = 8

Consider the initial value problem X′=AX, X(0)=[−4,-2], with A=[−6,0,1,−6] and X=[x(t)y(t)] (a) Find the eigenvalue λ,...

Consider the initial value problem X′=AX, X(0)=[−4,-2], with A=[−6,0,1,−6] and X=[x(t)y(t)] (a) Find the eigenvalue λ, an eigenvector V1, and a generalized eigenvector V2 for the coefficient matrix of this linear system. λ= , V1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ , V2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ $ (b) Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. X(t)=c1 ⎡⎣⎢⎢ ⎤⎦⎥⎥ + c2 ⎡⎣⎢⎢ ⎤⎦⎥⎥ (c) Solve the original initial value problem. x(t)=...

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Find the solution of the initial-value problem X′(t) = ( −8 −5 5 2 )X X0...

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Homework 1.1. (a) Find the solution of the initial value problem x' = x^(3/8) , x(0)=1...

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