Exponential and trigonometric functions practice question 8

Test each condition separately: differentiate to check $\dfrac{dy}{dx} = y$, and substitute $x = 0$ to check $y(0) = 3$.

Use $\dfrac{d}{dx}e^{x} = e^{x}$ and $\dfrac{d}{dx}3^{x} = 3^{x}\log 3$. A constant factor comes through differentiation unchanged, while an added constant differentiates to 0.