Question

if dy/dx=y+3>0 and y(0)=2 then y(log2) is equal to? a] 5 b]13 c]-2 d] 7​

Answer 1

Step-by-step explanation:

$\frac{dy}{dx} =( y + 3) \\ \\ \frac{dy}{(y + 3)} = dx \\ \\ integrating \: \: both \: \: sides \\ \\⇒ \int \frac{dy}{(y + 3)} = \int \: dx \\ \\ ⇒ log(y + 3) = x + c \: \: \: .............(1)$

Now

$y(0) = 2 \\ \\ put \: in \: \: eq \: \: 1 \\ \\ ⇒ log(y + 3) = x + c \\ \\ ⇒ log(2 + 3) = 0 + c \\ \\⇒ c = log(5) \\ \\ so \: \: eq. \: \: of \: \: curve \: \: is \: \\ \\ ⇒ log(y + 3) = x + log(5) \: \: ......(2)$

Hence

$so \: \: for \: \: y( log(2)) \: \\ \: put \:x = log(2) \: in \: \: eq \: 2 \\ \\ ⇒ log(y + 3) = log(2) + log(5) \\ \\⇒ log(y + 3) = log(2 \times 5) \\ \\ ⇒log(y + 3) = log(10) \\ \\⇒ y + 3 = 10 \\ \\⇒ y = 10 - 3 \\ \\ ⇒y = 7$