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What is a solution to the differential equation #dy/dx = 1 - 0.2y#?

Answer 1

Christopher Agresta

#y = alpha e^ (- 1/5 x) + 5#

#dy/dx = 1 - 0.2y#

# = 1/5 (5 - y)#

#int 1/(5 - y) dy = 1/5 int dx #

#int 1/(y-5) dy = -1/5 int dx #

#ln(y-5) = - 1/5 x + C#

#y-5 = exp (- 1/5 x + C)#

#= alpha e^ (- 1/5 x)# [where #alpha = e^C#]

#y = alpha e^ (- 1/5 x) + 5#

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Answer 2

Charles Arocha

The solution to the differential equation ( \frac{dy}{dx} = 1 - 0.2y ) is given by:

[ y(x) = \frac{5}{2} - C e^{-0.2x} ]

where ( C ) is an arbitrary constant.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.