If $\dfrac{dy}{dx} = y + 5$ and $y(0) = 4$ then $y(\log 2)$ is equal to

Given differential equation is $\dfrac{dy}{dx} = y + 5$

Separating the variables gives

$\dfrac{dy}{y + 5} = dx$

Integrating both sides gives

$\int \dfrac{dy}{y + 5} = \int dx$

$\log|y + 5| = x + C$

Using the initial condition $y(0) = 4$ gives

$\log(4 + 5) = 0 + C \Rightarrow C = \log 9$

Substituting $C$ back into the equation gives

$\log(y + 5) = x + \log 9$

$y + 5 = e^{x + \log 9} = 9e^x$

$y = 9e^x - 5$

Substituting $x = \log 2$ gives

$y(\log 2) = 9e^{\log 2} - 5$

$y(\log 2) = 9(2) - 5 = 13$

Answer: $13$