MASSIVEMARK PLAYGROUND: The Best ChatGPT Math Equation Renderer

This document was created using MassiveMark Playground as part of training series for our community on How to Copy Math Equations and Formula from ChatGPT Without Background

Equation (i)

$$\frac{dy}{dx} - cosx = 0$$

• Order: The highest derivative in the equation is $\frac{dy}{dx}$, which is the first derivative. So, the order is 1.
• Degree: The degree is the exponent of the highest-order derivative after the equation is made polynomial in derivatives. Here, $\frac{dy}{dx}$ is already in polynomial form, so the degree is 1.

Equation (ii)

$$xy\frac{d^{2}y}{dx^{2}} + x\left( \frac{dy}{dx} \right)^{2} - y\frac{dy}{dx} = 0$$

• Order: The highest derivative in the equation is $\frac{d^{2}y}{dx^{2}}$, which is the second derivative. So, the order is 2.
• Degree: The degree of $\frac{d^{2}y}{dx^{2}}$ is 1 (since the equation is already polynomial in derivatives). Therefore, the degree is 1.

Equation (iii)

• Order: The highest derivative in the equation is y^″, which is the second derivative. So, the order is 2.
• Degree: The equation involves the exponential function e^y′, which is not a polynomial in derivatives. Therefore, the degree is not defined.

1. (i) Order: 1, Degree: 1
2. (ii) Order: 2, Degree: 1
3. (iii) Order: 2, Degree: Not defined