Find the general solution of the differential equation. (Use C for any needed constant.) dy dx = 1 − y
1 answer:
Answer:
Step-by-step explanation:
Give the DE
dy/dx = 1-y
Using variable separable method
dy = (1-y)dx
dx = dy/(1-y)
Integrate both sides
∫dx = ∫dy/(1-y)
∫dy/(1-y)= ∫dx
-ln(1-y) = x+C
ln(1-y)^-1 = x+C
Apply e to both sides
e^ln(1-y)^-1 = e^,(x+C)
(1-y)^-1 = Ce^x
1/(1-y) = Ce^x
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