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))
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))