Question

Ds=(4t-3)dt, если s(0)=0

Answer 1

Ответ:

s = 2t² - 3t

Пошаговое объяснение:

s = 2t² - 3t + C

s(0) = C = 0

s = 2t² - 3t

Answer 2

To find the expression for s(t), we need to integrate the given differential equation with the initial condition s(0) = 0.

∫Ds = ∫(4t - 3) dt

Now, integrate both sides:

∫ds = ∫(4t - 3) dt

The integral of ds on the left side is simply s(t), and the integral of (4t - 3) dt on the right side is:

s(t) = 2t^2 - 3t + C

where C is the constant of integration.

Now, apply the initial condition s(0) = 0:

0 = 2(0)^2 - 3(0) + C 0 = C

So, the constant of integration (C) is 0. Therefore, the final expression for s(t) is:

s(t) = 2t^2 - 3t

This is the position function for the given differential equation with the initial condition s(0) = 0.