We want to solve the given differential equation. We will see that the correct option is A:
\(y(x) = 4*e^{4*x}\)
We know that:
\(\frac{dy}{dx} = 4y\\\\y(0) = 4\)
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:
\(y(x) = A*e^{4x}\)
Where A is a constant. Notice that if we derive the above function we get:
\(y'(x) = 4*A*e^{4x} = 4*y(x)\)
Now we use the initial value restriction, we know that when we evaluate this in x = 0, we should get 4, then:
\(y(0) = 4 = A*e^{4*0} = A\)
Then c = 4, then the equation is:
\(y(x) = 4*e^{4*x}\)
So the correct option is A.
If you want to learn more, you can read:
https://brainly.com/question/353770
