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Calculus help to solve the differential equation?
Solve the differential equation using the initial condition. Then find the exact value of f(1).
y = y - 1 y(0) = 3
I don t know how to do this so could you explain how to do this.
1 Answer
- Some BodyLv 74 years agoFavorite Answer
I'm guessing the y on the left side of the equal sign should be y'?
y' = y - 1
Write as dy/dx:
dy/dx = y - 1
Separate the variables (y's on one side and x's on the other):
dy / (y - 1) = dx
Integrate:
ln |y - 1| = x + C
Solve for y:
y - 1 = e^(x + C)
y = 1 + e^(x + C)
y = 1 + e^x e^C
e^C is just another constant, so:
y = 1 + C * e^x
Find C using the initial condition:
3 = 1 + C * e^0
2 = C
Substitute:
y = 1 + 2 * e^x
Finding f(1):
y = 1 + 2 * e^1
y = 1 + 2e
