Question

A differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation​ (ODE) or a partial differential equation​ (PDE), give the​ order, and indicate the independent and dependent variables. If the equation is an ordinary differential​ equation, indicate whether the equation is linear or nonlinear.

Answer 1

The question is incomplete. Here is the complete question.

A differential equation is given along with the field of problem area which it arises. Classify it as an ordinary differential equation (ODE) or a partial different equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

$x\frac{d^{2}y }{dx^{2} } + \frac{dy}{dx} + xy = 0$ (aerodynamics, stress analysis)

Answer and Step-by-step explanation: The differential equation described above is an Ordinary Differential Equation, because it has a definite set of variables: x and y.

It is of Second Order, since the highest derivative is of order 2: $\frac{d^{2}y }{dx^{2} }$

The differential equation is written as derivative of a function y in terms of x, which means: Independent Variable is X and Dependent Variable is Y.

As it is an ODE, the equation is Nonlinear, because y'' or $\frac{d^{2}y }{dx^{2} }$ is multiplied by a variable.