Find the particular solution that satisfies the differential equation and the initial condition.

1. f '(x) = 8x, f(0) = 7

2. f '(s) = 14s − 12s3, f(3) = 1

1)

2)

Step-by-step explanation:

Assuming that our function is for the first case and for the second case.

Part 1

We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition

And the final solution would be:

Part 2

We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition

And the final solution would be:

answer: i believe its b. if you sound out the sentences that sounds wrong.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.