Let c be a positive number. A differential equation of the form dy dt = ky1 + c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth. (a) Determine the solution that satisfies the initial condition y(0) = y0.

Differential equation is used to relate equations and their derivatives.

The solution that satisfies the initial condition is:

The differential equation is given as:

Multiply both sides by dt

Divide both sides by

Integrate both sides

Remove constants

Rewrite as:

Now, integrate both sides

This gives

At the initial condition,

So, we have:

Substitute in

Multiply through by c

Rewrite as:

Take inverse of both sides

Multiply both sides by -1

Take c-th root of both sides

Express as exponents

Express y as a function of t

Hence, the solution that satisfies the initial condition is:

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Step-by-step explanation:

We are given that  differential equation

Where k=Positive constant

c=Positive number

Initial condition

Substitute the value of initial condition

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it

step-by-step explanation:

yes it represnts a functio, their are not 2 of the same numbers on the both sides