Question

Explain how equality ${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$is relevant to Euler’s method.

Short answer

Ans: It is Proved that${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$ is relevant to Euler’s method.

Step-by-step solution

Step 1. Given information.

given,

${\left.\frac{dy}{dx}\right|}_{\left(x_k,y_k\right)}=\frac{\mathrm{\Delta }{y}_k}{\mathrm{\Delta }x}$

Step 2. Solution: