MHT-CET Full Test-8 Mathematics Que-33 Solution

Q.33. If \frac{dy}{dx}=y+3 and y(0) = 2, then y(log 2) =

A. 5

B. 7

C. 13

D. -2

Answer :- B. 7

Explanation :- \frac{dy}{dx}=y+3

\frac{dy}{y+3}=dx

Integrating on both sides, we get

\int \frac{dy}{y+3}=\int dx+c

log (y+3) = x+c –(i)

y=2 when x=0 … (Given )

log (2+3) = 0 + c

c= log 5

log(y+3) = x + log 5 [ from (i) ]

y+3 = 5e^x

y= 5e^x – 3

y(log 2) = 5 e^{log 2} – 3 = 10 – 3 = 7