Question

1. ) What are the initial conditions? (No work to show, but please give a brief explanation for why they are what they are.)

Answer 1

Initial conditions are any set of starting-point values belonging to or imposed upon the variables in an equation that has one or more arbitrary constants

Initial conditions are mostly used in differential equations.

As we know we get zero by differentiating a constant.So after integrating the differential equation we need to assume a constant which can be found with the help of initial conditions.

For e.g.

dy/dx=x

The solution can be y=x^{​​​​​​2}​​​​​ or y=x^{​​​​2} +c

So to find the value of c we need an initial condition i.e.,

At x=0,y is k(constant)