Ordinary Differential Equation Classification
An ordinary differential equation (ODE) is characterized by containing derivatives of only one independent variable.
The given differential equation is:
$2\frac{d^2z}{dx^2} + \frac{dz}{dx} + 3y = \sin x$
Observe the derivatives in the equation:
- $\frac{d^2z}{dx^2}$
- $\frac{dz}{dx}$
In these derivatives, '$x$' is the independent variable, as indicated by '$dx$' in the denominator. The presence of only one independent variable ('x') is the defining characteristic of an ordinary differential equation.
Therefore, the equation is considered ordinary because it has one independent variable.
Important Questions from Differential Equations
What is the order of the differential equation ?
What is the degree of the differential equation ?
A solution of the differential equation
\(\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 \) is
If y = \(\rm\left(\frac{1}{x}\right)^x \), then value of \(\rm e^e\left(\frac{d^2 y}{d x^2}\right)_{x=e}\) is:
The general solution of the differential equation ydx - xdy = 0
