Why ignores constant when applying integral into differential-equation.?

1. Why do we ignore the constant in an integrating factor?
2. What happens to constant when integrating?
3. What happens to constant in differential equation?

Why do we ignore the constant in an integrating factor?

Because when you multiply the equation by the integrating factor including an arbitrary constant, it just becomes a common constant factor across the whole equation. It can therefore be cancelled without any change to the solution.

What happens to constant when integrating?

Constant of Integration is added to the answer of the integration. This is written to represent the constant term of the original function, which could not be obtained through this anti-derivative process. The constant of integration can have arbitrary values and is written as +C.

What happens to constant in differential equation?

A differential equation has constant coefficients if only constant functions appear as coefficients in the associated homogeneous equation. A solution of a differential equation is a function that satisfies the equation. The solutions of a homogeneous linear differential equation form a vector space.