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

istupilo8k 2022-05-24 Answered
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?
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Answers (2)

bluayu0y
Answered 2022-05-25 Author has 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
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hawwend8u
Answered 2022-05-26 Author has 6 answers
Your assertion is not true. For example, if Q(x)=0, regardless of P(x), the equation is separable.
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