Question

Show that $y\left(x\right)=1.7e^{-2.1x}$is a solution of the differential equation $\frac{dy}{dx}=-2.1y$

Short answer

Hence proved

Step-by-step solution

Step 1. Given information

Given $y\left(x\right)=1.7e^{-2.1x}$

Step 2. Solve the given value

$$\begin{gathered} y\left(x\right)=1.7e^{-2.1x} \\ \frac{dy\left(x\right)}{dx}=\frac{d\left(1.7e^{-2.1x}\right)}{dx} \\ =1.7e^{-2.1x}\left(-2.1\right) \\ \frac{dy\left(x\right)}{dx}=-2.1y \end{gathered}$$

Hence proved