Solving a simple differential equation

[An1MuS]

I have had this question on my mind for a long time

When we solve a differential equation like this
$$\frac{dT}{dx}=0$$

Do we do this ?
$$\int\frac{dT}{dx}dx=\int0dx$$$$\int dT=\int0dx$$$$T =c_1$$

Because if we were to separate variables this doesn't work, we're just integrating both sides in respect to x, like when we multiply both sides of an equation by the same number to mantain the equality, but i haven't learned such a method.

THis came up because if we had

$$\frac{d^2T}{dx^2}=1$$

i thought we could do

$$\frac{d}{dx}\frac{dT}{dx}=1$$$$d(\frac{dT}{dx})=dx$$$$\int d(\frac{dT}{dx})=\int dx$$ $$\frac{dT}{dx}=x$$

etc which would be a real separation of variables, but it doesn't work in the first case.

What am i missing here?

 

[UltrafastPED]

dT/dx = 0 is equivalent to dT=0 dx, so you get the same result either way.

 

[An1MuS]

Ty :)