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Solve the initial value problem
by using the fundamental matrix
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Differential Equations: An Introduction to Modern Methods and Applications
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- Solve the initial value problem x' = by using the fundamental matrix X = Choose one Φ(t) = 1 4 - 5t e ( -5t -5 -16 1 cos 4t sin 4t 5t -4e-t sin 4t - 5t 3 )x, x(0) = ( ³ ) 2 e cos 4tarrow_forwardThe options for a and b are just can or can't be a solution.arrow_forwardSolve the initial value problem (요 6 -1 x, 11 -6 x' = x(0) = () 2 by using the fundamental matrix, 1 1le – e 1le - 11e-5t eAt -est + e-5t 10 +11e-5t X =arrow_forward
- This is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181arrow_forwardPlease solve everythingarrow_forwardPlease solve everythingarrow_forward
- Suppose that for a 2 x 2 matrix A, Au = 30 for u= • How is the pair (3, ū) called for a matrix A? Suppose further that the only non-zero vectors x, for which Ar = rx for some r, must be multiples of v above. • What more can you now saw about the number r = 3? Suppose further that Aw-3u = i for w = Write down the general solution of the differential equation x'(t) = Axarrow_forwardPlease help with this Ordinary Differential Equations problemarrow_forwardSuppose that for a 2 x 2 matrix A, AU = 3u for ū = • How is the pair (3, 0) called for a matrix A? Suppose further that the only non-zero vectors r, for which Ar = rz for some r, must be multiples of v above. • What more can you now saw about the number r = 3? Suppose further that Au-3w = ở for w = Write down the general solution of the differential equation x'(t) = Axarrow_forward
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