The family of solutions to the differential equation y ′ = −4xy3 is y = 1 √ C + 4x2 . Find the solution that satisfies the initial condition y(−2) = 4.

1. y = 4 p 1 + 16(x2 − 4)
2. y = 1 p 1 + 64(x 2 − 4)
3. y = 4 p 1 + 4(x2 − 4)
4. y = 4 p 1 + 64(x 2 − 4)
5. y = 1 p −4(x2 − 4) + 1

The correct option is 4

Step-by-step explanation:

The solution is given as

Now for the initial condition the value of C is calculated as

So the solution is given as

Simplifying the equation as

So the correct option is 4

the correct answer is 5

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!