Question

The general solution of $\frac{dy}{dx}=y$ is .

• A. $y=e^x$
• B. $y=e^x+c$
• C. $y=k{e}^x$
• D. $y=k{e}^x+c$

Answer 1

The correct option is C $y=k{e}^x$

We can observe that for $y=k{e}^x$,
$\frac{dy}{dx}=k{e}^x=y$
Hence, $y=k{e}^x$ is the general solution of the differential equation $\frac{dy}{dx}=y$.

Note that $y=e^x$ is a particular solution of the equation. It's not the general solution.