Hello
I am stuck on a problem with the following decription:
I do not exactly know what it means to show that the implicit solutions are determined via the ODE, and I cannot seem to show that the "!"-marked identities are true. I have tried two things:
(1) I have tried to establish each of the "!"-marked identities in the differential equation by computing the fraction with the partial derivatives:
(2) I have tried to use the folowing theorem to determine the solutions to the differential equation:
The theorem gives me the desired implicit equation, but with an integration constant added to it:
I feel like this gets me close to solving the exercise. However I am completely disregarding the integration limits in the theorem (Since my problem is not an initial-value-problem I think it makes sense, but I am not sure). Even if I am close, I still need to show that the "!"-marked identities are true.
Some inputs on this would be greatly appreciated!
I am stuck on a problem with the following decription:
I do not exactly know what it means to show that the implicit solutions are determined via the ODE, and I cannot seem to show that the "!"-marked identities are true. I have tried two things:
(1) I have tried to establish each of the "!"-marked identities in the differential equation by computing the fraction with the partial derivatives:
(2) I have tried to use the folowing theorem to determine the solutions to the differential equation:
The theorem gives me the desired implicit equation, but with an integration constant added to it:
I feel like this gets me close to solving the exercise. However I am completely disregarding the integration limits in the theorem (Since my problem is not an initial-value-problem I think it makes sense, but I am not sure). Even if I am close, I still need to show that the "!"-marked identities are true.
Some inputs on this would be greatly appreciated!