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

b. x- 48 =120

step-by-step explanation:

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.