MHT-CET Full Test-7 Mathematics Que-32 Solution

Q.32. 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 \Rightarrow \frac{dy}{y+3}=dx

Integrating both sides:
\int \frac{dy}{y+3}=\int dx

\Rightarrow \log(y+3)=x+c ……(i)

Given: y=2 when x=0, we substitute these values into equation (i):
\log(2+3)=0+c

\Rightarrow c=\log 5

Substituting c back into equation (i):
\log(y+3) = x + \log 5
\Rightarrow y+3 = e^x \cdot 5

\Rightarrow y = 5e^x - 3

Now, substituting x=\log 2:
y = 5e^{\log 2} - 3
= 5 \cdot 2 - 3

= 10 - 3 = 7

Thus, y(\log 2) = 7.