Solve the following initial value problem: dr/dt = -rt, r(0) = r0

Question

Solve the following initial value problem:

\(\frac{\text{dr}}{\text{dt}}=\) -rt, r(0) = r₀

Answer 1

Given differential equation  \(\frac{\text{dr}}{\text{dt}}=\) -rt

Find: Find the general solution of this differential equation.

\(=\frac{\text{dr}}{\text{dt}}=\) -rt

Integrating both side

Put t =0, r = r₀ in equation (i).

Now, log |r0| = -0 + C

log |r0| = C

Put the value of C in eq(i)