A differential equation is defined as an equation that includes the derivatives of one or more unknown functions, referred to as dependent variables, with respect to one or more independent variables. In this context, a dependent variable is one whose derivative is present in the equation, while an independent variable does not depend on other variables. For example, in the expression $$\frac{dy}{dx}$$, $y$ is the dependent variable and $x$ is the independent variable. Understanding these distinctions is crucial for solving differential equations effectively.
PREREQUISITESStudents of mathematics, educators teaching calculus, and professionals in fields requiring mathematical modeling, such as physics and engineering, will benefit from this discussion on differential equations.
an equation containing the derivatives of one or more unknown functions(or dependent variables), with respect to one or more independent variables.
find_the_fun said:My textbook defines differential equation as
Could someone explain what is meant by the part in parenthesis "dependent variables"? I don't see the difference.
So in the case $$\frac{dy}{dx}$$ the$$ x$$ is referred to as the independent variable?mathmari said:When a differential equation involves one or more derivatives with respect to a particular variable, that variable is called the independent variable.
find_the_fun said:So in the case $$\frac{dy}{dx}$$ the$$ x$$ is referred to as the independent variable?