Find the general solution of the given system. dx dt = 8x − y dy dt = 5x + 4y x(t), y(t) =

The general solution of given system is and .

Step-by-step explanation:

The given differential equations are

      .... (1)

     .... (2)

Differentiate both equations with respect to t.

                      ...... (3)

                   ..... (4)

Using equation (3) and (2).

                  (Using 1)

Using Quadratic formula

If , then

Therefore x(t) is defined as

Using equation (4) and (1).

                    (Using 2)

Using Quadratic formula

Therefore y(t) is defined as

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

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