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Choose the correct option.
The solution of (dy)/(dx) - y = 1, y(0) = 1 is given by:
The solution of $\frac{dy}{dx} - y = 1$, $y(0) = 1$ is given by:
- a$y = -e^x + 1$
- b$y = -e^{-x-1}$
- c$y = -1 + e^x$
- d$y = 2e^x - 1$
Answer
Answer
Correct option: d
Answer: (d) $y = 2e^x - 1$
Separating variables gives $\frac{dy}{1 + y} = dx$. Integrating yields $\ln(1 + y) = x + C$. Using $y(0) = 1$, we get $\ln 2 = C$, so $1 + y = 2e^x$, giving $y = 2e^x - 1$.