MA2132 - HW05

MA2132 - HW05 - x 5 Find a fundamental set of solutions to...

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Willis Thai MA2132 – Worksheet 5 1. Find a fundamental set of solutions to Ax x = , where = 6 2 4 2 1 2 4 2 2 A . 2. (a) Find the general solution to the nonhomogeneous system ) ( t f Ax x dt dx + = = , where = 1 2 2 1 A and = 0 ) ( t e t f . (b) Find the solution with the initial condition = 0 1 ) 0 ( x . 3. Find the general solution to ) ( t f Ax x + = , where = 1 1 2 3 A and = t e t f 2 0 ) ( . 4. Let = 2 0 0 3 1 0 4 3 1 A , = t e t f 2 2 0 0 ) ( , = 0 0 0 ) 0 ( x . a. Find a fundamental matrix to Ax dt dx = . b. Find a particular solution p x to ) ( t f Ax dt dx + = . c. Solve the initial value problem ) ( t f Ax dt dx + = where = 0 0 0 ) 0 (
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Unformatted text preview: x . 5. Find a fundamental set of solutions to each of the following: a. 108 63 31 9 ) 3 ( ) 4 ( ) 5 ( = ′ + ′ ′ + + + y y y y y . b. dx d D y D D D D D = = + − + + , ) 2 3 ( ) 20 4 ( 2 2 2 2 . 6. Consider a homogeneous linear differential equation with constant coefficients, having x xe x 2 3 + and ) 3 sin( 3 2 x x as its solutions. a. Find a fundamental set of solutions of the differential equation of minimum order. b. Write down the characteristic equation of the differential equation. c. Construct the differential equation....
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