Described above di erential the situationay y1 y0

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Unformatted text preview: t models equations. described above. di erential the situationAy y(1) = y0 where 4. Solve the the IVP y = The, relationship for arbitrary functions is more subtle. To see how, consider the followingsystem, if0any. example (b) Find the equilibrium solutions 2x the , if x of 14 2 cos(x) 3 . A = y solution a they0 (c) Find the general 1 (x) = ofnd 2x = system. 47 2 x , if x 0 2cos(xthe , if x < 0 two problems. If you cos(x) following * You may use Maple to help you with ) 5. Consider the DE y y1 (x)y= = A where x your worksheet(s) if x <your assignment. , with 0 5 .do, include a printout of 0 5 3x A= . cos(x) , x IR y ( x) y 8. Consider the system0y 2= 5 =, where x) A 3 cos( 3x multiplicity 2 1 (a) Use the definitionytoeigenvalue4of 2 (x),,yx(x)IR that has two linearly 2 )= (a) Show that A has one(xshow that yx) are linearly dependent 3 cos(41 3 the2general solution of the DE. A Hence independent eigenvectors. = 0 give . on x 0. 0 0 (4 (a) Use the definition to show that y1solve 2 (x) resulting equations and (b) Write the DE in component form,), x), y) are are linearly dependent (b) Use the definition show that y1 (x y2 (x the linearly dependent on on x that A...
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This homework help was uploaded on 02/22/2014 for the course AMATH 350 taught by Professor Davidhamsworth during the Fall '12 term at University of Waterloo, Waterloo.

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