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Unformatted text preview: dx dt =2 x + 3 y, dy dt = 2 xy d) Consider the system: x = 2 xy y = 3 x + y Estimate x (2) , y (2) using Eulers method with stepsize h = 1 if x (0) = 1 , y (0) = 2 . 5 Problem 3. a) Calculate the matrix products AB and BA. A = ± 1 + i 2 i ² B = ± i 2 0 3 ² b) Calculate the determinant of ± 3 + ii 6 2 ² 6 c) Find the eigenvalues and eigenvectors of ±1 29 5 ² d) Use the Eigenvalue Method to ﬁnd the general solution of dx dt =x + 13 y, dy dt =2 x + y 7 Problem 4. a) Find the general solution of x 00 =3 x + y y 00 = 2 x2 y b) dx dt = 3 x, dy dt =2 y Draw a phase portrait and Direction ﬁeld. 8 c) dx dt =5 y, dy dt =2 x Decide if (0 , 0) is stable. d) dx dt = x + x 22 xy, dy dt = y + 2 y 23 xy Find all critical points. 9...
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 Spring '07
 Stenstones?
 Eigenvalue, eigenvector and eigenspace, dt dy, 2y dt Draw

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