Write the given second order equation as its equivalent system of first order equations. u″+5u′+4u=0 u″+5u′+4u=0 use vv to represent the "velocity function", i. e. v=u′ (t) v=u′ (t). use vv and uu for the two functions, rather than u (t) u (t) and v (t) v (t).

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Mathematics

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7 April, 06:55

Write the given second order equation as its equivalent system of first order equations. u″+5u′+4u=0 u″+5u′+4u=0 use vv to represent the "velocity function", i. e. v=u′ (t) v=u′ (t). use vv and uu for the two functions, rather than u (t) u (t) and v (t) v (t).

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Matteo Decker · Answer 1

v = u', so v' = u'' and the original equation can be written

... v' + 5v + 4u = 0

Then the system of first-order equations is

... u' = v

... v' = - 5v - 4u