If dy/dx=4y and y=4 when x=0, then y=. a) 4e^4x. b) e^4x. c) 3+e^4x. d) 4+e^4x. e) 2x^2+4

We want to solve the given differential equation. We will see that the correct option is A:

We know that:

For a given function y(x).

Because the derivate is a constant times the original function, we know that the original function must be something like:

Where A is a constant. Notice that if we derive the above function we get:

Now we use the initial value restriction, we know that when we evaluate this in x = 0, we should get 4, then:

Then c = 4, then the equation is:

So the correct option is A.

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answer: 8d

step-by-step explanation:

45+5= 50+5=55+5=60