A question in my ODE textbook is as follows.

Determine whether the given first-order differential equation is linear in the indicated dependent variable.

$u dv+(v+uv-e^u)du = 0;$ in v; in u;

I feel as though I would be able to solve the question if I knew what the in v; in u; means.

In this question, what does in v; in u; mean? Is this a standard notation, and if so, what is it called?

  • $\begingroup$ For some basic information about writing math at this site see e.g. here, here, here and here. $\endgroup$ – Alice Ryhl Sep 17 '14 at 19:11
  • $\begingroup$ @Darksonn thanks, question edited. $\endgroup$ – LanceLafontaine Sep 17 '14 at 19:25

This is really a question about English writing. The question could be rewritten as

Determine whether the first-order differential equation $$u dv+(v+uv-e^u)du = 0$$ is linear in $u$. Determine also whether it is linear in $v$.


The notation in question looks to me like a shorthand way of asking these two questions:

  1. Is $u dv+(v+uv-e^u)du = 0$ linear in $u$?

  2. Is $u dv+(v+uv-e^u)du = 0$ linear in $v$?

Here I'm reading the word "in" as just a word in (mathematical) English, not a mathematical notation.





$\therefore$ This is a first-order ODE with the dependent variable $v$ .


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.