Find the particular solution of the differential equation...
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Find the particular solution of the differential equation...

[From: ] [author: ] [Date: 11-08-24] [Hit: ]
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Find the particular solution of the differential equation dy/dx + 2y = 6 satisfying the initial condition y(0) = 0 Help please! Thanks.

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dy/dx + 2y = 6

dy/dx = (6 - 2y)

dy/(6 - 2y) = dx

Integrating both sides:

-1/2*ln|6 - 2y| = x + C

6 - 2y = C*e^(-2x)

y = 3 + C*e^(-2x)

Plugging in the initial condition:

0 = C + 3 --> C = -3

y = 3(1 - e^(-2x))
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