Question

Identify ordinary differential equations

• A. $\frac{dy}{dx}+\frac{dz}{dx}=y+z$
• B. $\frac{dy}{dx}+x^{2}y=\sec x$
• C. $(\frac{dy}{dx}{)}^2=\ln \left(y\right)$
• D. $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}=x$

Answer 1

Answer: (A), (B), (C), (D)

$\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}=x$

We are given a set of differential equations. We want to find which among them are ordinary differential equations. Differential equations can be divided as ordinary differential equation and partial differential equation.
A differential equation is said to be ordinary if the dependent variables depend only on one independent variable say $x$.
It means we can have terms like $\frac{dy}{dx}$ and $\frac{dz}{dx}$ in the same differential equation. In these terms, the dependent variables $y$ and $z$ are dependent only on one variable $x$. But we can’t have terms like $\frac{df}{dz}$ and $\frac{df}{dy}$. Here, the dependent variable f depends on independent variables $z$ and $y$. ​All the equations given to us depend only on one independent variable.