Solve each of the following initial value problems:
, y(0) = 0
, y(0) = 0
Given and y(0) = 0
This is a first order linear differential equation of the form
Here, and
The integrating factor (I.F) of this differential equation is,
We have
Hence, the solution of the differential equation is,
We know
However, when x = 0, we have y = 0
⇒ 0 = (0 + c)e0
⇒ 0 = (c) × 1
∴ c = 0
By substituting the value of c in the equation for x, we get
Thus, the solution of the given initial value problem is