$\dfrac{dx}{dt}=u_0 e^{-kt}$
$dx = u_0 e^{-kt}dt$
$x(t)=\displaystyle{\int }u_0 e^{-kt}dt$
do this integration, include a constant of integration C, and solve for C given $x(0)=-L$
you'll find the formula you have pops right out.
I'm having trouble on a question in my calculus project about "Landing an airliner". It is not very complex and I understand everything but this problem.
They even give me the solution to the problem, just need to figure out how they got there.
"Integrate the relation u(t)=dx/dt and use the condition x(0)=-L to show that,
"
Shown below is what I'm trying to integrate to get x(t), which is shown above.
I'm in a loop here people , any help would be greatly, greatly appreciated.
$\dfrac{dx}{dt}=u_0 e^{-kt}$
$dx = u_0 e^{-kt}dt$
$x(t)=\displaystyle{\int }u_0 e^{-kt}dt$
do this integration, include a constant of integration C, and solve for C given $x(0)=-L$
you'll find the formula you have pops right out.