Solve the following initial value problem: An initial value problem consisting of the differential equation dr/dt = -rt and the initial condition r(0) = r_0.

Q43 of 462 Page 23

Solve the following initial value problem:

Given differential equation

Find: Find the general solution of this differential equation.

Integrating both side

= C .....(i)

Put t =0, r = r₀ in equation (i).

Now, C

= C

Put the value of C in eq(i)

Hence,

Solve the following initial value problem: