I like your way of explaining. You talk soft and clear and more over use chalk and black board unlike others using digital pen and don't even talk English properly. Keep it up bro
And now solving first order non-linear differential equations - I have never seen anyone cover as wide a range of questions as you do, and it's a joy to watch. Keep going and never stop learning 🫡
There are three main types of first order ordinary differential equations 1. Separable ODE 2. Linear ODE 3. Exact ODE Other types of first order ordinary differential equations which can be seen in textbooks can be reduced to this three types by substitution, integrating factor , introducing parameter
I'm assuming you are talking about time stamp 3:36. There is a constant of integration in both integrals, so technically, you can have a +C1 on the left integral, and a +C2 on the right, as you are suggesting, which gives us: arctanh(y) + C1 = -arctanh(t) + C2 However, we also can see that these two integration constants are not independent of each other. We can subtract C1 from both sides and get: arctanh(y) = -arctanh(t) + C2 - C1 Since it doesn't matter how we set C2 and C1 relative to each other, we can just combine them to one constant of integration, and get: arctanh(y) = -arctanh(t) + C Because this step happens in separable differential equations all the time, it is common to just keep it simple, and only add a +C on one of the integrals, but not the other.
Generally, you will only have an undetermined constant in the final general solution, for every order of differentiation involved in the highest derivative. This is how you can anticipate how many of the constants of integration to either absorb each other in intermediate steps, or ultimately cancel through other algebra as you post-process your integration results.
