Explain how to find the general solution to the given ODE, and the particular solution to the given IVP.

\[ -2 \, {y'} = 6 \, {y} ,\hspace{1em} y\big( \log\left(2\right) \big)= \frac{3}{8} \]

Then show how to verify that your particular solution is correct.

Answer:

\[ {y} = k e^{\left(-3 \, t\right)} \]

\[ {y} = 3 \, e^{\left(-3 \, t\right)} \]