Question

Find the general solution of the differential equation. (Use C for any needed constant.) dy dx = 1 − y

Answer 1

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