MatrixDiffEq

MatrixDiffEq - e e t t t t ' We can show that the solutions...

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MATRIX DIFFERENTIAL EQUATIONS Solving matrix first order differential equations given two vectors 25. p273 x x ' = - - 4 3 6 7 x 1 2 2 3 2 = e e t t x 2 5 5 3 = - - e e t t First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. We can verify that the given vectors are solutions of the given system by showing that the products of the coefficient matrix P and the vector function are equal to the differentials of the vector functions. Px x 1 2 2 2 2 1 4 3 6 7 3 2 6 4 = - - = = e e e e t t t t ' and Px x 2 5 5 5 5 2 4 3 6 7 3 5 15 = - - = - - = - - - - e e
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Unformatted text preview: e e t t t t ' We can show that the solutions x 1 and x 2 are linearly independent by showing that the Wronskian of the solutions is not equal to zero. 3 2 3 9 2 7 2 5 2 5 3 3 3 e e e e e e e t t t t t t t----- =-= To find the general solution we use the formula x x x ( ) ( ) ( ) t c t c t = + 1 1 2 2 substituting x 1 and x 2 x ( ) t c e e c e e t t t t = + --1 2 2 2 5 5 3 2 3 gives the general solution x ( ) t c e c e c e c e t t t t = --1 2 1 5 2 2 2 5 3 2 3 Tom Penick tomzap@eden.com October 24, 1997...
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