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Writing Prompt(s) One method for solving a system of first order linear differential equation such as x ?...

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Advance Math

Writing Prompt(s)

One method for solving a system of first order lineardifferential equation such as

x ? = a x + b y y ? = c x + d y

is to take the derivative of the first equation and use thesecond equation to ``decouple'' the system and create a secondorder equation, which we can solve using our previous techniques.Does this always work? If not, what conditions on the constants a,b, c, and d must be enforced? If it does work, we can then arriveat an equation for x(t). How do we proceed in finding an equationfor y(t)?

Answer & Explanation Solved by verified expert
4.3 Ratings (931 Votes)
Using the method of eliminationthe system of n linear differential equations reduces into a single nth order linear differential equationThis method is useful for simple cases like system of order 2 Now the given system is xaxby ycxdy Where a b c d are constant coefficients In    See Answer
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