For solving differential equations, especially the ones of the form
g(x)dx = h(y)dy
we solve the equation by 'integrating on both sides' to reveal the solution.
Understanding this for 'differentiating the equation on both sides' is relatively easy. We know that we can formulate an alternative equation in terms of differentials for the original equation involved and come out with a new 'differential' equation that holds because of the properties of the differentials.
But how does it work for Integration on both sides?? Am I missing any point here?? I have referred to multiple books but none give a satisfactory explanation. Integrating an equation on both sides seems really 'wrong', if I may dare to use the word.
Please help. I'm stuck with this thing and I can only begin to understand differential equations once this is cleared from my head.
Thank you very much !