Question

If y¢ = y + 1 and y(0) = 1 then values of y(ln 2) is-

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

3

Answer 2

$\frac{dy}{dx}$= y + 1

variable sep.

$\int_{}^{}\frac{dy}{y + 1}$= $\int_{}^{}{dx}$̃ log (y + 1) = x + c, y(0) =1

log 2 = c

So log (y + 1) = x + log 2 ̃ y (ln 2)

log (y +1) = 2 log 2 = log 4

y + 1 = 4

̃ y = 3