Question

Find the particular antiderivative that satisfies the following conditions: ∂x/∂t= 2e^t; x(0)= 7

Any help? I have no idea how to solve this...thanks in advance

Answer 1

transpose dt to the right

dx = 2e^t dt

Answer 2

then?

Answer 3

You have to integrate \(2e^t\). Do it please.

Answer 4

2 e^t + c

Answer 5

Your answer is \(2e^t+5\).

Answer 6

ok

Answer 7

the best way to do this is integrate both sides ,

by doing so you will get rid of partials, and the right side of equation will have a contant as a function of t, thats where you use you x(0)

Answer 8

i.e put t=0 after integrating, and sub x=7 to find value of constant