The standard form of a linear firs-order DE is d y </mrow> d

istupilo8k

istupilo8k

Answered question

2022-05-24

The standard form of a linear firs-order DE is
d y d x + P ( x ) y = Q ( x )
I think the equation is separable if and only if P ( x ) and Q ( x ) are constants, but I'm not sure. (Haven't found any counterexamples but also can't seem to prove it.) Can anyone confirm or deny that this is correct?

Answer & Explanation

bluayu0y

bluayu0y

Beginner2022-05-25Added 11 answers

For P = 0 and for any Q The DE is separable. You have also the case when P = λ Q Where λ is a constant, then it's also separable:
y + P ( x ) y = Q ( x )
y + λ Q ( x ) y = Q ( x )
y = Q ( x ) ( 1 λ y )
d y 1 λ y = Q ( x ) d x
hawwend8u

hawwend8u

Beginner2022-05-26Added 6 answers

Your assertion is not true. For example, if Q(x)=0, regardless of P(x), the equation is separable.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?