Two lines or equations are described in each part. Decide whether each system has one solution, no solution, or infinitely many
solutions. Show your work AND explain your reasoning for each of your answers.
(a) Line a has a rate of change of 7.
Line b has a rate of change of -7
(b) 2x + 3y = 5.5
4x + 6y = 11
(c) These two graphed lines:
(d) Line c and line d are parallel.
(a) Line a has a rate of change of 7.
Line b has a rate of change of -7
(b) 2x + 3y = 5.5
4x + 6y = 11
(c) These two graphed lines:
(d) Line c and line d are parallel.
1 answer:
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Answer:
Step-by-step explanation:
You have the following differential equation:
This equation can be written as:
where
If the differential equation is exact, it is necessary the following:
Then, you evaluate the partial derivatives:
The partial derivatives are equal, then, the differential equation is exact.
In order to obtain the solution of the equation you first integrate M or N:
(1)
Next, you derive the last equation respect to t:
however, the last derivative must be equal to M. From there you can calculate g(t):
Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:
where C is the constant of integration